Strong solutions for a compressible fluid model of Korteweg type
Annales de l'I.H.P. Analyse non linéaire, Tome 25 (2008) no. 4, pp. 679-696.
@article{AIHPC_2008__25_4_679_0,
     author = {Kotschote, Matthias},
     title = {Strong solutions for a compressible fluid model of {Korteweg} type},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {679--696},
     publisher = {Elsevier},
     volume = {25},
     number = {4},
     year = {2008},
     doi = {10.1016/j.anihpc.2007.03.005},
     mrnumber = {2436788},
     zbl = {1141.76053},
     language = {en},
     url = {https://www.numdam.org/articles/10.1016/j.anihpc.2007.03.005/}
}
TY  - JOUR
AU  - Kotschote, Matthias
TI  - Strong solutions for a compressible fluid model of Korteweg type
JO  - Annales de l'I.H.P. Analyse non linéaire
PY  - 2008
SP  - 679
EP  - 696
VL  - 25
IS  - 4
PB  - Elsevier
UR  - https://www.numdam.org/articles/10.1016/j.anihpc.2007.03.005/
DO  - 10.1016/j.anihpc.2007.03.005
LA  - en
ID  - AIHPC_2008__25_4_679_0
ER  - 
%0 Journal Article
%A Kotschote, Matthias
%T Strong solutions for a compressible fluid model of Korteweg type
%J Annales de l'I.H.P. Analyse non linéaire
%D 2008
%P 679-696
%V 25
%N 4
%I Elsevier
%U https://www.numdam.org/articles/10.1016/j.anihpc.2007.03.005/
%R 10.1016/j.anihpc.2007.03.005
%G en
%F AIHPC_2008__25_4_679_0
Kotschote, Matthias. Strong solutions for a compressible fluid model of Korteweg type. Annales de l'I.H.P. Analyse non linéaire, Tome 25 (2008) no. 4, pp. 679-696. doi : 10.1016/j.anihpc.2007.03.005. https://www.numdam.org/articles/10.1016/j.anihpc.2007.03.005/

[1] Amann H., Operator-valued Fourier multipliers, vector-valued Besov spaces, and applications, Math. Nachr. 186 (1997) 5-56. | MR | Zbl

[2] Anderson D.M., Mcfadden G.B., Wheeler A.A., Diffuse-interface methods in fluid mech, Ann. Rev. Fluid Mech. 30 (1998) 139-165. | MR

[3] Bresch D., Desjardins B., Lin C., On some compressible fluid models: Korteweg, lubrication, and shallow water systems, Comm. Partial Differential Equations 28 (3-4) (2003) 843-868. | MR | Zbl

[4] Cahn J.W., Hilliard J.E., Free energy of a nonuniform system, I. Interfacial free energy, J. Chem. Phys. 28 (1998) 258-267.

[5] Danchin R., Desjardins B., Existence of solutions for compressible fluid models of Korteweg type, Ann. Inst. H. Poincaré Anal. Non Linéaire 18 (1) (2001) 97-133. | EuDML | Numdam | MR | Zbl

[6] Denk R., Hieber M., Prüss J., R-boundedness and problems of elliptic and parabolic type, Mem. Amer. Math. Soc. 166 (788) (2003), viii+114 pp. | MR | Zbl

[7] Dore G., Venni A., On the closedness of the sum of two closed operators, Math. Z. 196 (1987) 189-201. | EuDML | MR | Zbl

[8] Dunn J.E., Serrin J., On the thermomechanics of interstitial working, Arch. Rational Mech. Anal. 88 (2) (1985) 95-133. | MR | Zbl

[9] Escher J., Prüss J., Simonett G., A new approach to the regularity of solutions for parabolic equations, in: Evolution Equations, Lecture Notes in Pure and Appl. Math., vol. 234, Dekker, New York, 2003, pp. 167-190. | MR | Zbl

[10] Gurtin M.E., Polignone D., Vinals J., Two-phase binary fluids and immiscible fluids described by an order parameter, Math. Models Methods Appl. Sci. 6 (6) (1996) 815-831. | MR | Zbl

[11] Hattori H., Li D., The existence of global solutions to a fluid dynamic model for materials for Korteweg type, J. Partial Differential Equations 9 (4) (1996) 323-342. | MR | Zbl

[12] Hattori H., Li D., Global solutions of a high-dimensional system for Korteweg materials, J. Math. Anal. Appl. 198 (1) (1996) 84-97. | MR | Zbl

[13] Kalton N., Weis L., The H-calculus and sums of closed operators, Math. Ann. 321 (2) (2001) 319-345. | MR | Zbl

[14] M. Kotschote, Strong well-posedness of a model for an ionic exchange process, Thesis, Martin-Luther-Universität Halle-Wittenberg, 2003.

[15] Ladyzenskaya O.A., Solonikov V.A., Uralceva N.N., Linear and Quasilinear Equations of Parabolic Type, Transl. Math. Monographs, Amer. Math. Soc., Providence, RI, 1968.

[16] Lancien F., Lancien G., Le Merdy C., A joint functional calculus for sectorial operators with commuting resolvents, Proc. London Math. Soc. 77 (1998) 387-414. | MR | Zbl

[17] Prüss J., Maximal regularity for abstract parabolic problems with inhomogeneous boundary data in Lp-spaces, Math. Bohem. 127 (2) (2002) 311-327. | EuDML | MR | Zbl

[18] Prüss J., Sohr H., On operators with bounded imaginary powers in Banach spaces, Math. Z. 203 (1990) 429-452. | EuDML | MR | Zbl

[19] Sobolevskii P.E., Coerciveness inequalities for abstract parabolic equations, Soviet Math. (Doklady) 5 (1964) 894-897. | MR | Zbl

[20] Triebel H., Interpolation Theory, Function Spaces, Differential Operators, North-Holland, 1978. | MR | Zbl

[21] Triebel H., Theory of Function Spaces, Geest & Portig K.-G., Leipzig, 1983. | MR | Zbl

[22] Zacher R., Maximal regularity of type Lp for abstract parabolic Volterra equations, J. Evol. Equ. 5 (1) (2005) 79-103. | MR | Zbl

[23] R. Zacher, Quasilinear parabolic integro-differential equations with nonlinear boundary conditions, preprint. | MR | Zbl

  • Ju, Qiangchang; Xu, Jianjun Long time existence for the non-isentropic slightly compressible fluid model of Korteweg type, Acta Mathematica Scientia, Volume 45 (2025) no. 2, p. 416 | DOI:10.1007/s10473-025-0209-4
  • Bagus Suhada, Dede; Maryani, Sri; Renny, Renny; Triyani, Triyani; Hendriya Guswanto, Bambang; Kartiwi, Mira; Jan, C.; Anwer, I.; Li, L.; Ferse, S.; Nishi, M.; Puangprakhon, P. Whole space case for solution formula of Korteweg type fluid motion in R3, E3S Web of Conferences, Volume 609 (2025), p. 03003 | DOI:10.1051/e3sconf/202560903003
  • Song, Zihao; Xu, Jiang Decay of higher order derivatives for L solutions to the compressible fluid model of Korteweg type, Journal of Mathematical Analysis and Applications, Volume 541 (2025) no. 2, p. 128694 | DOI:10.1016/j.jmaa.2024.128694
  • Yao, Zheng-an; Yin, Xuan Convergence rate of the three-dimensional compressible fluid models of Korteweg type to the Navier–Stokes system, Journal of Mathematical Physics, Volume 66 (2025) no. 2 | DOI:10.1063/5.0234180
  • Wu, Wanping; Zhang, Yinghui Space-time Decay Rate for the Compressible Navier–Stokes–Korteweg System in R3, Bulletin of the Iranian Mathematical Society, Volume 50 (2024) no. 5 | DOI:10.1007/s41980-024-00916-6
  • Maryani, Sri; Murata, Miho R-Bounded Operator Families Arising from a Compressible Fluid Model of Korteweg Type with Surface Tension in the Half-Space, Complex Analysis and Operator Theory, Volume 18 (2024) no. 8 | DOI:10.1007/s11785-024-01618-x
  • Plaza, Ramón G.; Zhelyazov, Delyan Well-posedness and decay structure of a quantum hydrodynamics system with Bohm potential and linear viscosity, Journal of Mathematical Physics, Volume 65 (2024) no. 8 | DOI:10.1063/5.0172774
  • Inna, Suma The existence of RR‐bounded solution operator for Navier–Stokes–Korteweg model with slip boundary conditions in half space, Mathematical Methods in the Applied Sciences, Volume 47 (2024) no. 11, p. 8581 | DOI:10.1002/mma.10033
  • Dong, Wenchao Stability of viscous contact wave for the full compressible Navier–Stokes–Korteweg equations with large perturbation, Nonlinearity, Volume 37 (2024) no. 9, p. 095019 | DOI:10.1088/1361-6544/ad61b4
  • Chen, Kaile; Liang, Yunyun; Zhang, Nengqiu Global existence of strong solutions to compressible Navier-Stokes-Korteweg equations with external potential force, AIMS Mathematics, Volume 8 (2023) no. 11, p. 27712 | DOI:10.3934/math.20231418
  • Keim, Jens; Munz, Claus-Dieter; Rohde, Christian A relaxation model for the non-isothermal Navier-Stokes-Korteweg equations in confined domains, Journal of Computational Physics, Volume 474 (2023), p. 111830 | DOI:10.1016/j.jcp.2022.111830
  • Song, Zihao; Xu, Jiang Global existence and analyticity of L solutions to the compressible fluid model of Korteweg type, Journal of Differential Equations, Volume 370 (2023), p. 101 | DOI:10.1016/j.jde.2023.06.011
  • Giovangigli, Vincent; Calvez, Yoann Le; Nabet, Flore Symmetrization and Local Existence of Strong Solutions for Diffuse Interface Fluid Models, Journal of Mathematical Fluid Mechanics, Volume 25 (2023) no. 4 | DOI:10.1007/s00021-023-00825-4
  • Tang, Tong; Wei, Xu; Ling, Zhi On the blow‐up phenomena of the compressible Navier‐Stokes‐Korteweg system with degenerate viscosity, Mathematical Methods in the Applied Sciences, Volume 46 (2023) no. 6, p. 6470 | DOI:10.1002/mma.8919
  • Zhou, Yanping; Wang, Xun Energy equality for weak solutions of the compressible Navier–Stokes–Korteweg equations with general pressure law in a bounded domain, Results in Applied Mathematics, Volume 20 (2023), p. 100397 | DOI:10.1016/j.rinam.2023.100397
  • Li, Yeping; Xu, Rui; Chen, Zhengzheng Asymptotic stability of a nonlinear wave for the compressible Navier–Stokes–Korteweg equations in the half space, Zeitschrift für angewandte Mathematik und Physik, Volume 74 (2023) no. 4 | DOI:10.1007/s00033-023-02064-z
  • Jiang, Xiaopan; Wu, Zhigang Pointwise Space-Time Behavior of a Compressible Navier-Stokes-Korteweg System in Dimension Three, Acta Mathematica Scientia, Volume 42 (2022) no. 5, p. 2113 | DOI:10.1007/s10473-022-0522-0
  • Kawashima, Shuichi; Shibata, Yoshihiro; Xu, Jiang Dissipative structure for symmetric hyperbolic-parabolic systems with Korteweg-type dispersion, Communications in Partial Differential Equations, Volume 47 (2022) no. 2, p. 378 | DOI:10.1080/03605302.2021.1983596
  • Hong, Hakho Stability of stationary solutions and viscous shock wave in the inflow problem for isentropic Navier-Stokes-Korteweg system, Journal of Differential Equations, Volume 314 (2022), p. 518 | DOI:10.1016/j.jde.2022.01.012
  • Plaza, Ramón G.; Valdovinos, José M. Dissipative structure of one-dimensional isothermal compressible fluids of Korteweg type, Journal of Mathematical Analysis and Applications, Volume 514 (2022) no. 2, p. 126336 | DOI:10.1016/j.jmaa.2022.126336
  • Kobayashi, Takayuki; Murata, Miho; Saito, Hirokazu Resolvent Estimates for a Compressible Fluid Model of Korteweg Type and Their Application, Journal of Mathematical Fluid Mechanics, Volume 24 (2022) no. 1 | DOI:10.1007/s00021-021-00646-3
  • Shi, Weixuan; Song, Zihao; Zhang, Jianzhong Large-Time Behavior of Solutions in the Critical Spaces for the Non-isentropic Compressible Navier–Stokes Equations with Capillarity, Journal of Mathematical Fluid Mechanics, Volume 24 (2022) no. 3 | DOI:10.1007/s00021-022-00693-4
  • Li, Yeping; Chen, Zhengzheng Large-Time Behavior of Solutions to an Inflow Problem for the Compressible Navier–Stokes–Korteweg Equations in the Half Space, Journal of Mathematical Fluid Mechanics, Volume 24 (2022) no. 4 | DOI:10.1007/s00021-022-00736-w
  • Yu, Yanghai; Yang, Xiaolei; Wu, Xing Global smooth solutions of 3‐D Navier‐Stokes‐Korteweg equations with large initial data, Mathematical Methods in the Applied Sciences, Volume 45 (2022) no. 10, p. 6165 | DOI:10.1002/mma.8163
  • Song, Zihao; Xu, Jiang Global Dynamics of the Compressible Fluid Model of the Korteweg Type in Hybrid Besov Spaces, Mathematics, Volume 11 (2022) no. 1, p. 174 | DOI:10.3390/math11010174
  • Li, Yeping; Tang, Jing; Yu, Shengqi Asymptotic stability of rarefaction wave for the compressible Navier‐Stokes‐Korteweg equations in the half space, Proceedings of the Royal Society of Edinburgh: Section A Mathematics, Volume 152 (2022) no. 3, p. 756 | DOI:10.1017/prm.2021.32
  • Yu, Yanghai; Zhou, Mulan On the Well-Posedness of the Compressible Navier-Stokes-Korteweg System with Special Viscosity and Capillarity, Results in Mathematics, Volume 77 (2022) no. 4 | DOI:10.1007/s00025-022-01717-1
  • Kobayashi, Takayuki; Tsuda, Kazuyuki Time Decay Estimate with Diffusion Wave Property and Smoothing Effect for Solutions to the Compressible Navier-Stokes-Korteweg System, Funkcialaj Ekvacioj, Volume 64 (2021) no. 2, p. 163 | DOI:10.1619/fesi.64.163
  • Kawashima, Shuichi; Shibata, Yoshihiro; Xu, Jiang The L energy methods and decay for the compressible Navier-Stokes equations with capillarity, Journal de Mathématiques Pures et Appliquées, Volume 154 (2021), p. 146 | DOI:10.1016/j.matpur.2021.08.009
  • Yu, Yanghai; Wu, Xing Global strong solution of 2D Navier–Stokes–Korteweg system, Mathematical Methods in the Applied Sciences, Volume 44 (2021) no. 14, p. 11231 | DOI:10.1002/mma.7484
  • Saito, Hirokazu Existence of R‐bounded solution operator families for a compressible fluid model of Korteweg type on the half‐space, Mathematical Methods in the Applied Sciences, Volume 44 (2021) no. 2, p. 1744 | DOI:10.1002/mma.6875
  • Li, Yeping; Zhu, Peicheng Asymptotic stability of the stationary solution to an out-flow problem for the Navier–Stokes–Korteweg equations of compressible fluids, Nonlinear Analysis: Real World Applications, Volume 57 (2021), p. 103193 | DOI:10.1016/j.nonrwa.2020.103193
  • Qin, Yuming; Zhang, Jianlin; Wang, Yang; Su, Xing Global existence, uniqueness and exponential stability of solutions for the one-dimensional Navier–Stokes equations with capillarity, Nonlinear Analysis: Real World Applications, Volume 58 (2021), p. 103222 | DOI:10.1016/j.nonrwa.2020.103222
  • Li, Yeping; Luo, Zhen Stability of the planar rarefaction wave to three-dimensional Navier–Stokes–Korteweg equations of compressible fluids, Nonlinearity, Volume 34 (2021) no. 5, p. 2689 | DOI:10.1088/1361-6544/abb544
  • Chen, Zhengzheng; Li, Yeping Asymptotic Behavior of Solutions to An Impermeable Wall Problem of the Compressible Fluid Models of Korteweg Type with Density-dependent Viscosity and Capillarity, SIAM Journal on Mathematical Analysis, Volume 53 (2021) no. 2, p. 1434 | DOI:10.1137/20m1340319
  • Hitz, Timon; Keim, Jens; Munz, Claus-Dieter; Rohde, Christian A parabolic relaxation model for the Navier-Stokes-Korteweg equations, Journal of Computational Physics, Volume 421 (2020), p. 109714 | DOI:10.1016/j.jcp.2020.109714
  • Saito, Hirokazu On the maximal L-L regularity for a compressible fluid model of Korteweg type on general domains, Journal of Differential Equations, Volume 268 (2020) no. 6, p. 2802 | DOI:10.1016/j.jde.2019.09.040
  • Zhang, Shunhang A class of global large solutions to the compressible Navier–Stokes–Korteweg system in critical Besov spaces, Journal of Evolution Equations, Volume 20 (2020) no. 4, p. 1531 | DOI:10.1007/s00028-020-00565-2
  • Li, Yeping; Zhu, Peicheng Zero-viscosity–capillarity limit toward rarefaction wave with vacuum for the Navier–Stokes–Korteweg equations of compressible fluids, Journal of Mathematical Physics, Volume 61 (2020) no. 11 | DOI:10.1063/5.0006290
  • Huang, Feimin; Hong, Hakho; Shi, Xiaoding Existence of smooth solutions for the compressible barotropic Navier‐Stokes‐Korteweg system without increasing pressure law, Mathematical Methods in the Applied Sciences, Volume 43 (2020) no. 8, p. 5073 | DOI:10.1002/mma.6252
  • Hong, Hakho Stationary solutions to outflow problem for 1-D compressible fluid models of Korteweg type: Existence, stability and convergence rate, Nonlinear Analysis: Real World Applications, Volume 53 (2020), p. 103055 | DOI:10.1016/j.nonrwa.2019.103055
  • Wang, Yinxia; Wang, Yu-Zhu Asymptotic profiles and convergence rate of the compressible fluid models of Korteweg type, Zeitschrift für angewandte Mathematik und Physik, Volume 71 (2020) no. 2 | DOI:10.1007/s00033-020-1269-x
  • Hong, Hakho Strong solutions for the compressible barotropic fluid model of Korteweg type in the bounded domain, Zeitschrift für angewandte Mathematik und Physik, Volume 71 (2020) no. 3 | DOI:10.1007/s00033-020-01306-8
  • Gao, Jincheng; Lyu, Zeyu; Yao, Zheng-an Lower bound of decay rate for higher-order derivatives of solution to the compressible fluid models of Korteweg type, Zeitschrift für angewandte Mathematik und Physik, Volume 71 (2020) no. 4 | DOI:10.1007/s00033-020-01330-8
  • Gao, Zhensheng; Liang, Yan; Tan, Zhong A Global Existence Result for Korteweg System in the Critical LP Framework, Acta Mathematica Scientia, Volume 39 (2019) no. 6, p. 1639 | DOI:10.1007/s10473-019-0614-7
  • Saito, Hirokazu Compressible Fluid Model of Korteweg Type with Free Boundary Condition: Model Problem, Funkcialaj Ekvacioj, Volume 62 (2019) no. 3, p. 337 | DOI:10.1619/fesi.62.337
  • Wang, Yinxia Asymptotic Profiles and Convergence Rates of the Linearized Compressible Navier–Stokes– Korteweg System, Mathematics, Volume 7 (2019) no. 3, p. 287 | DOI:10.3390/math7030287
  • Li, Yeping; Liao, Jie Existence of strong solutions to the stationary compressible Navier–Stokes–Korteweg equations with large external force, Nonlinear Analysis: Real World Applications, Volume 47 (2019), p. 204 | DOI:10.1016/j.nonrwa.2018.09.002
  • Hou, Xiaofeng; Peng, Hongyun; Zhu, Changjiang Global classical solutions to the 3D Navier–Stokes–Korteweg equations with small initial energy, Analysis and Applications, Volume 16 (2018) no. 01, p. 55 | DOI:10.1142/s0219530516500123
  • Abels, Helmut; Garcke, Harald Weak Solutions and Diffuse Interface Models for IncompressibleTwo-Phase Flows, Handbook of Mathematical Analysis in Mechanics of Viscous Fluids (2018), p. 1267 | DOI:10.1007/978-3-319-13344-7_29
  • Watanabe, Keiichi Compressible–Incompressible Two-Phase Flows with Phase Transition: Model Problem, Journal of Mathematical Fluid Mechanics, Volume 20 (2018) no. 3, p. 969 | DOI:10.1007/s00021-017-0352-3
  • Li, Yeping; Peng, Sihao; Wang, Shu Some limit analysis of a three dimensional viscous compressible capillary model for plasma, Mathematical Methods in the Applied Sciences, Volume 41 (2018) no. 14, p. 5535 | DOI:10.1002/mma.5096
  • Wang, Yu‐Zhu; Wang, Yinxia Optimal decay estimate of mild solutions to the compressible Navier‐Stokes‐Korteweg system in the critical Besov space, Mathematical Methods in the Applied Sciences, Volume 41 (2018) no. 18, p. 9592 | DOI:10.1002/mma.5316
  • Hou, Xiaofeng; Peng, Hongyun; Zhu, Changjiang Global well-posedness of the 3D non-isothermal compressible fluid model of Korteweg type, Nonlinear Analysis: Real World Applications, Volume 43 (2018), p. 18 | DOI:10.1016/j.nonrwa.2018.02.002
  • Abels, Helmut; Daube, Johannes; Kraus, Christiane; Kröner, Dietmar The Sharp-Interface Limit for the Navier–Stokes–Korteweg Equations, Theory, Numerics and Applications of Hyperbolic Problems I, Volume 236 (2018), p. 1 | DOI:10.1007/978-3-319-91545-6_1
  • Giesselmann, Jan; Zacharenakis, Dimitrios A Posteriori Analysis for the Euler–Korteweg Model, Theory, Numerics and Applications of Hyperbolic Problems I, Volume 236 (2018), p. 631 | DOI:10.1007/978-3-319-91545-6_48
  • Tang, Tong; Gao, Hongjun On the Euler-Korteweg System with Free Boundary Condition, Acta Applicandae Mathematicae, Volume 150 (2017) no. 1, p. 111 | DOI:10.1007/s10440-017-0097-2
  • Giesselmann, Jan; Lattanzio, Corrado; Tzavaras, Athanasios E. Relative Energy for the Korteweg Theory and Related Hamiltonian Flows in Gas Dynamics, Archive for Rational Mechanics and Analysis, Volume 223 (2017) no. 3, p. 1427 | DOI:10.1007/s00205-016-1063-2
  • Freistühler, Heinrich; Kotschote, Matthias Phase-Field and Korteweg-Type Models for the Time-Dependent Flow of Compressible Two-Phase Fluids, Archive for Rational Mechanics and Analysis, Volume 224 (2017) no. 1, p. 1 | DOI:10.1007/s00205-016-1065-0
  • Lai, Jin; Wen, Huanyao; Yao, Lei Vanishing capillarity limit of the non-conservative compressible two-fluid model, Discrete Continuous Dynamical Systems - B, Volume 22 (2017) no. 4, p. 1361 | DOI:10.3934/dcdsb.2017066
  • Chertock, Alina; Degond, Pierre; Neusser, Jochen An asymptotic-preserving method for a relaxation of the Navier–Stokes–Korteweg equations, Journal of Computational Physics, Volume 335 (2017), p. 387 | DOI:10.1016/j.jcp.2017.01.030
  • Hou, Xiaofeng; Yao, Lei; Zhu, Changjiang Vanishing capillarity limit of the compressible non-isentropic Navier–Stokes–Korteweg system to Navier–Stokes system, Journal of Mathematical Analysis and Applications, Volume 448 (2017) no. 1, p. 421 | DOI:10.1016/j.jmaa.2016.11.014
  • Haspot, Boris Global strong solution for the Korteweg system with quantum pressure in dimension N2 N ≥ 2, Mathematische Annalen, Volume 367 (2017) no. 1-2, p. 667 | DOI:10.1007/s00208-016-1391-4
  • Abels, Helmut; Garcke, Harald; Grün, Günther; Metzger, Stefan Diffuse Interface Models for Incompressible Two-Phase Flows with Different Densities, Transport Processes at Fluidic Interfaces (2017), p. 203 | DOI:10.1007/978-3-319-56602-3_8
  • Freistühler, Heinrich; Kotschote, Matthias Dynamical Stability of Diffuse Phase Boundaries in Compressible Fluids, Transport Processes at Fluidic Interfaces (2017), p. 355 | DOI:10.1007/978-3-319-56602-3_14
  • Diehl, Dennis; Kremser, Jenny; Kröner, Dietmar; Rohde, Christian Numerical solution of Navier–Stokes–Korteweg systems by Local Discontinuous Galerkin methods in multiple space dimensions, Applied Mathematics and Computation, Volume 272 (2016), p. 309 | DOI:10.1016/j.amc.2015.09.080
  • Tang, Tong; Gao, Hongjun On the compressible Navier-Stokes-Korteweg equations, Discrete and Continuous Dynamical Systems - Series B, Volume 21 (2016) no. 8, p. 2745 | DOI:10.3934/dcdsb.2016071
  • Abels, Helmut; Garcke, Harald Weak Solutions and Diffuse Interface Models for Incompressible Two-Phase Flows, Handbook of Mathematical Analysis in Mechanics of Viscous Fluids (2016), p. 1 | DOI:10.1007/978-3-319-10151-4_29-1
  • Haspot, Boris Existence of global strong solution for Korteweg system with large infinite energy initial data, Journal of Mathematical Analysis and Applications, Volume 438 (2016) no. 1, p. 395 | DOI:10.1016/j.jmaa.2016.01.047
  • Li, Yeping; Luo, Zhen Zero‐viscosity‐capillarity limit to rarefaction waves for the 1D compressible Navier–Stokes–Korteweg equations, Mathematical Methods in the Applied Sciences, Volume 39 (2016) no. 18, p. 5513 | DOI:10.1002/mma.3934
  • Chen, Zhengzheng Large-time behavior of smooth solutions to the isothermal compressible fluid models of Korteweg type with large initial data, Nonlinear Analysis, Volume 144 (2016), p. 139 | DOI:10.1016/j.na.2016.06.009
  • Tang, Tong Blow-up of Smooth Solutions to the Compressible Barotropic Navier-Stokes-Korteweg Equations on Bounded Domains, Acta Applicandae Mathematicae, Volume 136 (2015) no. 1, p. 55 | DOI:10.1007/s10440-014-9884-1
  • Gao, Jincheng; Zou, Yang; Yao, Zheng-an Long-time behavior of solution for the compressible Navier–Stokes–Korteweg equations in R3, Applied Mathematics Letters, Volume 48 (2015), p. 30 | DOI:10.1016/j.aml.2015.03.006
  • Cai, Hong; Tan, Zhong; Xu, Qiuju Time periodic solutions to Navier-Stokes-Korteweg system with friction, Discrete and Continuous Dynamical Systems, Volume 36 (2015) no. 2, p. 611 | DOI:10.3934/dcds.2016.36.611
  • Wang, Yudong; Cheng, Peng; Yang, Jianwei Asymptotic limit of a Navier-Stokes-Korteweg system with density-dependent viscosity, Electronic Research Announcements in Mathematical Sciences, Volume 22 (2015) no. 0, p. 20 | DOI:10.3934/era.2015.22.20
  • Neusser, J.; Rohde, C.; Schleper, V. Relaxation of the Navier–Stokes–Korteweg equations for compressible two‐phase flow with phase transition, International Journal for Numerical Methods in Fluids, Volume 79 (2015) no. 12, p. 615 | DOI:10.1002/fld.4065
  • Tian, Lulu; Xu, Yan; Kuerten, J.G.M.; van der Vegt, J.J.W. A local discontinuous Galerkin method for the (non)-isothermal Navier–Stokes–Korteweg equations, Journal of Computational Physics, Volume 295 (2015), p. 685 | DOI:10.1016/j.jcp.2015.04.025
  • Chen, Zhengzheng; Chai, Xiaojuan; Dong, Boqing; Zhao, Huijiang Global classical solutions to the one-dimensional compressible fluid models of Korteweg type with large initial data, Journal of Differential Equations, Volume 259 (2015) no. 8, p. 4376 | DOI:10.1016/j.jde.2015.05.023
  • Chen, Zhengzheng; He, Lin; Zhao, Huijiang Nonlinear stability of traveling wave solutions for the compressible fluid models of Korteweg type, Journal of Mathematical Analysis and Applications, Volume 422 (2015) no. 2, p. 1213 | DOI:10.1016/j.jmaa.2014.09.050
  • Cai, Hong; Tan, Zhong; Xu, Qiuju Time periodic solutions of the non-isentropic compressible fluid models of Korteweg type, Kinetic Related Models, Volume 8 (2015) no. 1, p. 29 | DOI:10.3934/krm.2015.8.29
  • Freistühler, Heinrich Phase Transitions and Traveling Waves in Compressible Fluids, Archive for Rational Mechanics and Analysis, Volume 211 (2014) no. 1, p. 189 | DOI:10.1007/s00205-013-0682-0
  • Wang, Wenjun; Yao, Lei Vanishing viscosity limit to rarefaction waves for the full compressible fluid models of Korteweg type, Communications on Pure and Applied Analysis, Volume 13 (2014) no. 6, p. 2331 | DOI:10.3934/cpaa.2014.13.2331
  • Tan, Zhong; Zhang, Xu; Wang, Huaqiao Asymptotic behavior of Navier-Stokes-Korteweg with friction in R3, Discrete Continuous Dynamical Systems - A, Volume 34 (2014) no. 5, p. 2243 | DOI:10.3934/dcds.2014.34.2243
  • Chen, Zhengzheng; Zhao, Huijiang Existence and nonlinear stability of stationary solutions to the full compressible Navier–Stokes–Korteweg system, Journal de Mathématiques Pures et Appliquées, Volume 101 (2014) no. 3, p. 330 | DOI:10.1016/j.matpur.2013.06.005
  • Chen, Zhengzheng; Xiong, Linjie; Meng, Yijie Convergence to the superposition of rarefaction waves and contact discontinuity for the 1-D compressible Navier–Stokes–Korteweg system, Journal of Mathematical Analysis and Applications, Volume 412 (2014) no. 2, p. 646 | DOI:10.1016/j.jmaa.2013.10.073
  • Brenner, Howard Conduction-only transport phenomena in compressible bivelocity fluids: Diffuse interfaces and Korteweg stresses, Physical Review E, Volume 89 (2014) no. 4 | DOI:10.1103/physreve.89.043020
  • Bian, Dongfen; Yao, Lei; Zhu, Changjiang Vanishing Capillarity Limit of the Compressible Fluid Models of Korteweg Type to the Navier–Stokes Equations, SIAM Journal on Mathematical Analysis, Volume 46 (2014) no. 2, p. 1633 | DOI:10.1137/130942231
  • Tan, Zhong; Zhang, Rongfang Optimal decay rates of the compressible fluid models of Korteweg type, Zeitschrift für angewandte Mathematik und Physik, Volume 65 (2014) no. 2, p. 279 | DOI:10.1007/s00033-013-0331-3
  • Braack, Malte; Prohl, Andreas Stable discretization of a diffuse interface model for liquid-vapor flows with surface tension, ESAIM: Mathematical Modelling and Numerical Analysis, Volume 47 (2013) no. 2, p. 401 | DOI:10.1051/m2an/2012032
  • Liu, Ju; Gomez, Hector; Evans, John A.; Hughes, Thomas J.R.; Landis, Chad M. Functional entropy variables: A new methodology for deriving thermodynamically consistent algorithms for complex fluids, with particular reference to the isothermal Navier–Stokes–Korteweg equations, Journal of Computational Physics, Volume 248 (2013), p. 47 | DOI:10.1016/j.jcp.2013.04.005
  • Chen, Zhengzheng; Xiao, Qinghua Nonlinear stability of viscous contact wave for the one‐dimensional compressible fluid models of Korteweg type, Mathematical Methods in the Applied Sciences, Volume 36 (2013) no. 17, p. 2265 | DOI:10.1002/mma.2750
  • Li, Yeping Global existence and optimal decay rate of the compressible Navier–Stokes–Korteweg equations with external force, Journal of Mathematical Analysis and Applications, Volume 388 (2012) no. 2, p. 1218 | DOI:10.1016/j.jmaa.2011.11.006
  • Tan, Zhong; Wang, Huaqiao; Xu, Jiankai Global existence and optimal L2 decay rate for the strong solutions to the compressible fluid models of Korteweg type, Journal of Mathematical Analysis and Applications, Volume 390 (2012) no. 1, p. 181 | DOI:10.1016/j.jmaa.2012.01.028
  • Chen, Zhengzheng Asymptotic stability of strong rarefaction waves for the compressible fluid models of Korteweg type, Journal of Mathematical Analysis and Applications, Volume 394 (2012) no. 1, p. 438 | DOI:10.1016/j.jmaa.2012.04.008
  • Abels, Helmut Strong Well-posedness of a Diffuse Interface Model for a Viscous, Quasi-incompressible Two-phase Flow, SIAM Journal on Mathematical Analysis, Volume 44 (2012) no. 1, p. 316 | DOI:10.1137/110829246
  • Kotschote, Matthias Dynamics of Compressible Non-isothermal Fluids of Non-Newtonian Korteweg Type, SIAM Journal on Mathematical Analysis, Volume 44 (2012) no. 1, p. 74 | DOI:10.1137/110821202
  • Wang, Yanjin; Tan, Zhong Optimal decay rates for the compressible fluid models of Korteweg type, Journal of Mathematical Analysis and Applications, Volume 379 (2011) no. 1, p. 256 | DOI:10.1016/j.jmaa.2011.01.006
  • Haspot, Boris Existence of Global Weak Solution for Compressible Fluid Models of Korteweg Type, Journal of Mathematical Fluid Mechanics, Volume 13 (2011) no. 2, p. 223 | DOI:10.1007/s00021-009-0013-2
  • Michoski, C.; Evans, J.A.; Schmitz, P.G.; Vasseur, A. Quantum hydrodynamics with trajectories: The nonlinear conservation form mixed/discontinuous Galerkin method with applications in chemistry, Journal of Computational Physics, Volume 228 (2009) no. 23, p. 8589 | DOI:10.1016/j.jcp.2009.08.011

Cité par 99 documents. Sources : Crossref