On the three-dimensional Euler equations with a free boundary subject to surface tension
Annales de l'I.H.P. Analyse non linéaire, Tome 22 (2005) no. 6, pp. 753-781.
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     title = {On the three-dimensional {Euler} equations with a free boundary subject to surface tension},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
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Schweizer, Ben. On the three-dimensional Euler equations with a free boundary subject to surface tension. Annales de l'I.H.P. Analyse non linéaire, Tome 22 (2005) no. 6, pp. 753-781. doi : 10.1016/j.anihpc.2004.11.001. https://www.numdam.org/articles/10.1016/j.anihpc.2004.11.001/

[1] Beale J.T., Large time regularity of viscous surface waves, Arch. Rat. Mech. Anal. 84 (1984) 307-352. | MR | Zbl

[2] Beyer K., Günther M., On the Cauchy problem for a capillary drop. I. Irrotational motion, Math. Methods Appl. Sci. 21 (12) (1998) 1149-1183. | MR | Zbl

[3] Chen X., Friedman A., A bubble in ideal fluid with gravity, J. Differential Equations 81 (1989) 136-166. | MR | Zbl

[4] Christodoulou D., Lindblad H., On the motion of the free surface of a liquid, Comm. Pure Appl. Math. 53 (12) (2000) 1536-1602. | MR | Zbl

[5] Ebin D.G., The equations of motion of a perfect fluid with free boundary are not well posed, Comm. Partial Differential Equations 12 (1987) 1175-1201. | MR | Zbl

[6] Evans L.C., Partial Differential Equations, Grad. Stud. Math., vol. 19, Amer. Math. Soc., 1998. | MR | Zbl

[7] Iguchi T., Tanaka N., Tani A., On the two-phase free boundary problem for two-dimensional water waves, Math. Ann. 309 (2) (1997) 199-223. | MR | Zbl

[8] Iguchi T., Tanaka N., Tani A., On a free boundary problem for an incompressible ideal fluid in two space dimensions, Adv. Math. Sci. Appl. 9 (1) (1999) 415-472. | MR | Zbl

[9] Kato T., Ponce G., Well-posedness of the Euler and Navier-Stokes equations in Lebesgue spaces, Rev. Mat. Iberoamericana 2 (1986) 73-88. | MR | Zbl

[10] Lions J.L., Magenes E., Non-Homogeneous Boundary Value Problems and Applications, I, Grundlehren Math. Wiss., vol. 181, Springer-Verlag, 1972. | Zbl

[11] Ogawa M., Tani A., Free boundary problem for an incompressible ideal fluid with surface tension, Math. Models Methods Appl. Sci. 12 (12) (2002) 1725-1740. | MR | Zbl

[12] Okazawa N., The Euler equation on a bounded domain as a quasilinear evolution equation, Commun. Appl. Nonlinear Anal. 3 (3) (1996) 107-113. | MR | Zbl

[13] Renardy M., An existence theorem for a free surface flow problem with open boundaries, Comm. Partial Differential Equations 17 (1992) 1387-1405. | MR | Zbl

[14] Schweizer B., A two-component flow with a viscous and an inviscid fluid, Comm. Partial Differential Equations 25 (2000) 887-901. | MR | Zbl

[15] Triebel H., Theory of Function Spaces, Monographs Math., vol. 78, Birkhäuser, 1983. | MR | Zbl

[16] Triebel H., Theory of Function Spaces II, Monographs Math., vol. 84, Birkhäuser, 1992. | MR | Zbl

[17] Wagner A., On the Bernoulli free boundary problem with surface tension, in: Athanasopoulos I. (Ed.), Free boundary problems: theory and applications, CRC Res. Notes Math., vol. 409, Chapman & Hall, 1999, pp. 246-251. | MR | Zbl

[18] Wu S., Well-posedness in Sobolev spaces of the full water wave problem in 2-D, Invent. Math. 130 (1) (1997) 39-72. | MR | Zbl

[19] Wu S., Well-posedness in Sobolev spaces of the full water wave problem in 3-D, J. Amer. Math. Soc. 12 (2) (1999) 445-495. | MR | Zbl

  • Hu, Xiaoling A priori estimates for the free boundary problem of rotating Euler–Boussinesq equations with surface tension, Nonlinear Analysis: Real World Applications, Volume 84 (2025), p. 104306 | DOI:10.1016/j.nonrwa.2024.104306
  • Berti, Massimiliano; Maspero, Alberto; Murgante, Federico Hamiltonian Birkhoff Normal Form for Gravity-Capillary Water Waves with Constant Vorticity: Almost Global Existence, Annals of PDE, Volume 10 (2024) no. 2 | DOI:10.1007/s40818-024-00182-z
  • Hu, Zhongtian; Luo, Chenyun; Yao, Yao Small Scale Creation for 2D Free Boundary Euler Equations with Surface Tension, Annals of PDE, Volume 10 (2024) no. 2 | DOI:10.1007/s40818-024-00179-8
  • Ming, Mei; Wang, Chao Local Well-Posedness of the Capillary-Gravity Water Waves with Acute Contact Angles, Archive for Rational Mechanics and Analysis, Volume 248 (2024) no. 5 | DOI:10.1007/s00205-024-02019-2
  • Alazard, Thomas The Water-Wave Equations in Eulerian Coordinates, Free Boundary Problems in Fluid Dynamics, Volume 54 (2024), p. 1 | DOI:10.1007/978-3-031-60452-2_1
  • Gu, Xumin; Luo, Chenyun; Zhang, Junyan Local well-posedness of the free-boundary incompressible magnetohydrodynamics with surface tension, Journal de Mathématiques Pures et Appliquées, Volume 182 (2024), p. 31 | DOI:10.1016/j.matpur.2023.12.009
  • Aydin, Mustafa Sencer; Kukavica, Igor; Ożański, Wojciech S.; Tuffaha, Amjad Construction of the free-boundary 3D incompressible Euler flow under limited regularity, Journal of Differential Equations, Volume 394 (2024), p. 209 | DOI:10.1016/j.jde.2024.02.027
  • Julin, Vesa; La Manna, Domenico Angelo A Priori Estimates for the Motion of Charged Liquid Drop: A Dynamic Approach via Free Boundary Euler Equations, Journal of Mathematical Fluid Mechanics, Volume 26 (2024) no. 3 | DOI:10.1007/s00021-024-00883-2
  • Agrawal, Siddhant Angled Crested Like Water Waves with Surface Tension II: Zero Surface Tension Limit, Memoirs of the American Mathematical Society, Volume 293 (2024) no. 1458 | DOI:10.1090/memo/1458
  • Fu, Jie; Hao, Chengchun; Yang, Siqi; Zhang, Wei A Beale–Kato–Majda criterion for free boundary incompressible ideal magnetohydrodynamics, Journal of Mathematical Physics, Volume 64 (2023) no. 9 | DOI:10.1063/5.0167954
  • Kukavica, I; Ożański, W S Local-in-time existence of a free-surface 3D Euler flow with H 2+δ initial vorticity in a neighborhood of the free boundary, Nonlinearity, Volume 36 (2023) no. 1, p. 636 | DOI:10.1088/1361-6544/aca5e3
  • Berti, Massimiliano; Maspero, Alberto; Murgante, Federico Hamiltonian Paradifferential Birkhoff Normal Form for Water Waves, Regular and Chaotic Dynamics, Volume 28 (2023) no. 4-5, p. 543 | DOI:10.1134/s1560354723040032
  • Wang, Jingjie; Wen, Xiaoyong; Yuen, Manwai Blowup for regular solutions and C1 solutions of the two-phase model in RN with a free boundary, AIMS Mathematics, Volume 7 (2022) no. 8, p. 15313 | DOI:10.3934/math.2022839
  • Foukroun, N.; Hernane-Boukari, D.; Ait-Yahia-Djouadi, R. Solvability of a three-dimensional free surface flow problem over an obstacle, Applicable Analysis, Volume 101 (2022) no. 2, p. 554 | DOI:10.1080/00036811.2020.1754401
  • Zhang, Junyan Local Well-Posedness and Incompressible Limit of the Free-Boundary Problem in Compressible Elastodynamics, Archive for Rational Mechanics and Analysis, Volume 244 (2022) no. 3, p. 599 | DOI:10.1007/s00205-022-01774-4
  • Zheng, Fan Long‐Term Regularity of 3D Gravity Water Waves, Communications on Pure and Applied Mathematics, Volume 75 (2022) no. 5, p. 1074 | DOI:10.1002/cpa.21985
  • Agrawal, Siddhant Angled Crested Like Water Waves with Surface Tension: Wellposedness of the Problem, Communications in Mathematical Physics, Volume 383 (2021) no. 3, p. 1409 | DOI:10.1007/s00220-020-03934-7
  • Ming, Mei; Wang, Chao Water‐Waves Problem with Surface Tension in a Corner Domain II: The Local Well‐Posedness, Communications on Pure and Applied Mathematics, Volume 74 (2021) no. 2, p. 225 | DOI:10.1002/cpa.21916
  • Wang, Zhan; Yang, Jiaqi Well-posedness of Electrohydrodynamic Interfacial Waves under Tangential Electric Field, SIAM Journal on Mathematical Analysis, Volume 53 (2021) no. 2, p. 2567 | DOI:10.1137/19m1285986
  • Luo, Chenyun; Zhang, Junyan A priori Estimates for the Incompressible Free-Boundary Magnetohydrodynamics Equations with Surface Tension, SIAM Journal on Mathematical Analysis, Volume 53 (2021) no. 2, p. 2595 | DOI:10.1137/19m1283938
  • Alazard, Thomas; Ifrim, Mihaela; Tataru, Daniel A Morawetz Inequality for Gravity-Capillary Water Waves at Low Bond Number, Water Waves, Volume 3 (2021) no. 3, p. 429 | DOI:10.1007/s42286-020-00044-8
  • Disconzi, Marcelo M.; Luo, Chenyun On the Incompressible Limit for the Compressible Free-Boundary Euler Equations with Surface Tension in the Case of a Liquid, Archive for Rational Mechanics and Analysis, Volume 237 (2020) no. 2, p. 829 | DOI:10.1007/s00205-020-01516-4
  • Luo, Chenyun; Zhang, Junyan A regularity result for the incompressible magnetohydrodynamics equations with free surface boundary, Nonlinearity, Volume 33 (2020) no. 4, p. 1499 | DOI:10.1088/1361-6544/ab60d9
  • Ming, Mei; Wang, Chao Water Waves Problem with Surface Tension in a Corner Domain I: A Priori Estimates with Constrained Contact Angle, SIAM Journal on Mathematical Analysis, Volume 52 (2020) no. 5, p. 4861 | DOI:10.1137/19m1239957
  • Lian, Jiali Global well-posedness of the free-surface incompressible Euler equations with damping, Journal of Differential Equations, Volume 267 (2019) no. 2, p. 1066 | DOI:10.1016/j.jde.2019.02.002
  • Disconzi, Marcelo M; Kukavica, Igor A priori estimates for the free-boundary Euler equations with surface tension in three dimensions, Nonlinearity, Volume 32 (2019) no. 9, p. 3369 | DOI:10.1088/1361-6544/ab0b0d
  • Disconzi, Marcelo M.; Kukavica, Igor; Tuffaha, Amjad A Lagrangian Interior Regularity Result for the Incompressible Free Boundary Euler Equation with Surface Tension, SIAM Journal on Mathematical Analysis, Volume 51 (2019) no. 5, p. 3982 | DOI:10.1137/18m1216808
  • Berti, Massimiliano; Delort, Jean-Marc Introduction, Almost Global Solutions of Capillary-Gravity Water Waves Equations on the Circle, Volume 24 (2018), p. 1 | DOI:10.1007/978-3-319-99486-4_1
  • Berti, Massimiliano; Delort, Jean-Marc Reduction to a Constant Coefficients Operator and Proof of the Main Theorem, Almost Global Solutions of Capillary-Gravity Water Waves Equations on the Circle, Volume 24 (2018), p. 113 | DOI:10.1007/978-3-319-99486-4_5
  • Kukavica, Igor; Tuffaha, Amjad A sharp regularity result for the Euler equation with a free interface, Asymptotic Analysis, Volume 106 (2018) no. 2, p. 121 | DOI:10.3233/asy-171459
  • Disconzi, Marcelo M.; Kukavica, Igor On the local existence for the Euler equations with free boundary for compressible and incompressible fluids, Comptes Rendus. Mathématique, Volume 356 (2018) no. 3, p. 306 | DOI:10.1016/j.crma.2018.02.002
  • Düll, Wolf-Patrick On the Mathematical Description of Time-Dependent Surface Water Waves, Jahresbericht der Deutschen Mathematiker-Vereinigung, Volume 120 (2018) no. 2, p. 117 | DOI:10.1365/s13291-017-0173-6
  • Elgindi, Tarek; Lee, Donghyun Uniform regularity for free-boundary Navier–Stokes equations with surface tension, Journal of Hyperbolic Differential Equations, Volume 15 (2018) no. 01, p. 37 | DOI:10.1142/s0219891618500030
  • Lian, Jiali Zero surface tension limit of the free-surface incompressible Euler equations with damping, Nonlinear Analysis, Volume 169 (2018), p. 218 | DOI:10.1016/j.na.2017.12.012
  • Ionescu, A. D.; Pusateri, F. Recent advances on the global regularity for irrotational water waves, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Volume 376 (2018) no. 2111, p. 20170089 | DOI:10.1098/rsta.2017.0089
  • Kukavica, Igor; Tuffaha, Amjad; Vicol, Vlad On the Local Existence and Uniqueness for the 3D Euler Equation with a Free Interface, Applied Mathematics Optimization, Volume 76 (2017) no. 3, p. 535 | DOI:10.1007/s00245-016-9360-6
  • Masmoudi, Nader; Rousset, Frederic Uniform Regularity and Vanishing Viscosity Limit for the Free Surface Navier–Stokes Equations, Archive for Rational Mechanics and Analysis, Volume 223 (2017) no. 1, p. 301 | DOI:10.1007/s00205-016-1036-5
  • Lee, Donghyun Uniform Estimate of Viscous Free-Boundary Magnetohydrodynamics with Zero Vacuum Magnetic Field, SIAM Journal on Mathematical Analysis, Volume 49 (2017) no. 4, p. 2710 | DOI:10.1137/16m1089794
  • Kukavica, Igor; Tuffaha, Amjad; Vicol, Vlad; Wang, Fei On the Existence for the Free Interface 2D Euler Equation with a Localized Vorticity Condition, Applied Mathematics Optimization, Volume 73 (2016) no. 3, p. 523 | DOI:10.1007/s00245-016-9346-4
  • Ignatova, Mihaela; Kukavica, Igor On the local existence of the free-surface Euler equation with surface tension, Asymptotic Analysis, Volume 100 (2016) no. 1-2, p. 63 | DOI:10.3233/asy-161386
  • Gu, Xumin; Lei, Zhen Local well-posedness of the three dimensional compressible Euler–Poisson equations with physical vacuum, Journal de Mathématiques Pures et Appliquées, Volume 105 (2016) no. 5, p. 662 | DOI:10.1016/j.matpur.2015.11.010
  • Disconzi, Marcelo M.; Ebin, David G. The free boundary Euler equations with large surface tension, Journal of Differential Equations, Volume 261 (2016) no. 2, p. 821 | DOI:10.1016/j.jde.2016.03.029
  • Ambrose, David M. Vortex Sheet Formulations and Initial Value Problems: Analysis and Computing, Lectures on the Theory of Water Waves (2016), p. 140 | DOI:10.1017/cbo9781316411155.009
  • Ming, Mei; Rousset, Frederic; Tzvetkov, Nikolay Multi-solitons and Related Solutions for the Water-waves System, SIAM Journal on Mathematical Analysis, Volume 47 (2015) no. 1, p. 897 | DOI:10.1137/140960220
  • Kukavica, Igor; Tuffaha, Amjad A Regularity Result for the Incompressible Euler Equation with a Free Interface, Applied Mathematics Optimization, Volume 69 (2014) no. 3, p. 337 | DOI:10.1007/s00245-013-9221-5
  • Disconzi, Marcelo M.; Ebin, David G. On the Limit of Large Surface Tension for a Fluid Motion with Free Boundary, Communications in Partial Differential Equations, Volume 39 (2014) no. 4, p. 740 | DOI:10.1080/03605302.2013.865058
  • Disconzi, Marcelo On a linear problem arising in dynamic boundaries, Evolution Equations Control Theory, Volume 3 (2014) no. 4, p. 627 | DOI:10.3934/eect.2014.3.627
  • Secchi, Paolo; Trakhinin, Yuri Well-posedness of the plasma–vacuum interface problem, Nonlinearity, Volume 27 (2014) no. 1, p. 105 | DOI:10.1088/0951-7715/27/1/105
  • Kukavica, Igor; Tuffaha, Amjad On the 2D free boundary Euler equation, Evolution Equations Control Theory, Volume 1 (2012) no. 2, p. 297 | DOI:10.3934/eect.2012.1.297
  • Gu, Xumin; Lei, Zhen Well-posedness of 1-D compressible Euler–Poisson equations with physical vacuum, Journal of Differential Equations, Volume 252 (2012) no. 3, p. 2160 | DOI:10.1016/j.jde.2011.10.019
  • Alazard, T.; Burq, N.; Zuily, C. Low regularity Cauchy theory for the water-waves problem: canals and swimming pools, Journées équations aux dérivées partielles (2012), p. 1 | DOI:10.5802/jedp.75
  • Kukavica, Igor; Tuffaha, Amjad Well-posedness for the compressible Navier–Stokes–Lamé system with a free interface, Nonlinearity, Volume 25 (2012) no. 11, p. 3111 | DOI:10.1088/0951-7715/25/11/3111
  • Shatah, Jalal; Zeng, Chongchun Local Well-Posedness for Fluid Interface Problems, Archive for Rational Mechanics and Analysis, Volume 199 (2011) no. 2, p. 653 | DOI:10.1007/s00205-010-0335-5
  • Alazard, T.; Burq, N.; Zuily, C. On the water-wave equations with surface tension, Duke Mathematical Journal, Volume 158 (2011) no. 3 | DOI:10.1215/00127094-1345653
  • Cheng, C. H. Arthur; Coutand, Daniel; Shkoller, Steve On the Limit as the Density Ratio Tends to Zero for Two Perfect Incompressible Fluids Separated by a Surface of Discontinuity, Communications in Partial Differential Equations, Volume 35 (2010) no. 5, p. 817 | DOI:10.1080/03605300903503115
  • Shatah, Jalal; Zeng, Chongchun Geometry and a priori estimates for free boundary problems of the Euler's equation, Communications on Pure and Applied Mathematics, Volume 61 (2008) no. 5, p. 698 | DOI:10.1002/cpa.20213
  • Coutand, Daniel; Shkoller, Steve Well-posedness of the free-surface incompressible Euler equations with or without surface tension, Journal of the American Mathematical Society, Volume 20 (2007) no. 3, p. 829 | DOI:10.1090/s0894-0347-07-00556-5
  • Schweizer, B.; Bodea, S.; Surulescu, C.; Surovtsova, I. Fluid Flows and Free Boundaries, Reactive Flows, Diffusion and Transport (2007), p. 5 | DOI:10.1007/978-3-540-28396-6_1

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