@article{ASNSP_1997_4_25_3-4_807_0, author = {Temam, Roger and Wang, Xiaoming}, title = {On the behavior of the solutions of the {Navier-Stokes} equations at vanishing viscosity}, journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze}, pages = {807--828}, publisher = {Scuola normale superiore}, volume = {Ser. 4, 25}, number = {3-4}, year = {1997}, mrnumber = {1655543}, zbl = {1043.35127}, language = {en}, url = {http://www.numdam.org/item/ASNSP_1997_4_25_3-4_807_0/} }
TY - JOUR AU - Temam, Roger AU - Wang, Xiaoming TI - On the behavior of the solutions of the Navier-Stokes equations at vanishing viscosity JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze PY - 1997 SP - 807 EP - 828 VL - 25 IS - 3-4 PB - Scuola normale superiore UR - http://www.numdam.org/item/ASNSP_1997_4_25_3-4_807_0/ LA - en ID - ASNSP_1997_4_25_3-4_807_0 ER -
%0 Journal Article %A Temam, Roger %A Wang, Xiaoming %T On the behavior of the solutions of the Navier-Stokes equations at vanishing viscosity %J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze %D 1997 %P 807-828 %V 25 %N 3-4 %I Scuola normale superiore %U http://www.numdam.org/item/ASNSP_1997_4_25_3-4_807_0/ %G en %F ASNSP_1997_4_25_3-4_807_0
Temam, Roger; Wang, Xiaoming. On the behavior of the solutions of the Navier-Stokes equations at vanishing viscosity. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 25 (1997) no. 3-4, pp. 807-828. http://www.numdam.org/item/ASNSP_1997_4_25_3-4_807_0/
[Al] Existence and asymptotic representation of weak solutions to the flowing problem under the condition of regular slippage on solid walls, Siberian Math. J. 35 (1994), 209-229. | MR | Zbl
,[As] Zero-Viscosity Limit of the Incompressible Navier-Stokes Equations 1, 2, Preprint, University of Kyoto, 1997.
,[BP] Fluid Dynamics", Cours de l'Ecole d'Ete de Physique Théorique, Les Houches Gordon and Breach Science Publishers, New-York, 1977. | MR | Zbl
- , "[BC1] Small viscosity asymptotics for the inertial range of local structure and for the wall region of wall-bounded turbulent shear flow, Proc. Natl. Acad. Sci., Applied Mathematics 93 (1996). | Zbl
- ,[BC2] Scaling laws and zero viscosity limits for wall-bounded shear flows and for local structure in developed turbulence. Preprint, Center for Pure and Applied Mathematics, University of California at Berkeley, n° PAM-678, 1996. | MR
- ,[Ba] An Introduction to Fluid Dynamics", Cambridge University Press, Cambridge, 1967. | MR | Zbl
, "[BKM] Remarks on the breakdown of smooth solutions for the 3D Euler equations, Comm. Math. Phys. 94 (1984), 61-66. | MR | Zbl
- - ,[Ch] Turbulence as a near-equilibrium process, in Lecture in Applied Mathematics 31 (1996), 235-249, AMS, Providence. | MR | Zbl
,[CW] Inviscid limit for vortex patches, Nonlinearity 8 (1995), 735-742. | MR | Zbl
- ,[EE] Blow-up of Solutions of the Unsteady Prandtl's Equation, preprint, 1996.
- ,[EM] Groups of diffeomorphisms and the motion of an incompressible fluid, Arch. Rational Mech. Anal. 46 (1972), 241-279. | MR
- ,[E] Asymptotic Analysis of Singular Perturbations ", North-Holland, 1979. | MR | Zbl
, "[F] Considerations regarding the mathematical basis for Prandtl's boundary layer theory, Arch. Rational Mech. Anal. 38 (1967), 184-216. | MR | Zbl
,[Ge] Méthodes Asymptotiques en Mécanique des Fluides ", in [BP]. | Zbl
, "[Gr] The Theory of Rotating Fluids", Cambridge Univ. Press, Cambridge, 1968. | MR | Zbl
, "[K1] Remarks on the Zero Viscosity Limit for Nonstationary Navier-Stokes Flows with Boundary", in Seminar on PDE, edited by S. S. Chern, Springer, N.Y., 1984. | MR
, "[K2] On the classical solutions of two dimensional nonstationary Euler equations, Arch. Rational Mech. Anal 25 (1967), 188-200. | MR | Zbl
,[La] Matched Asymptotics Expansion, Ideas and Techniques ", Springer-Verlag, New-York, 1988. | MR | Zbl
, "[LL] Fluid Mechanics", Addison-Wesley, New-York, 1953.
- , "[Lc] Grundlagen der Hydromechanik", Springer-Verlag, 1923. | JFM | MR | Zbl
, "[Lo1] Quelques Méthodes de Résolution des Problèmes aux Limites non Linéaires ", Dunod, Paris, 1969. | MR | Zbl
, "[Lo2] Perturbations singulières dans les problèmes aux limites et en contrôle optimal, Lecture Notes in Math. 323 Springer-Verlag, New-York, 1973. | MR | Zbl
,[M] "Compressible fluid flow and systems of conservation laws in several space variables", Springer-Verlag, New-York, 1984. | MR | Zbl
,[O] The Prandtl system of equations in boundary layer theory, Dokl. Akad. Nauk S.S.S.R. 150, 4(3) (1963), 583-586. | Zbl
,[Pr] Veber Flüssigkeiten bei sehr kleiner Reibung, Verh. III Intern. Math. Kongr. Heidelberg (1905), 484-491, Teuber, Leibzig. | JFM
,[SC] Zero viscosity limit for analytic solutions of the Navier-Stokes equation on a half-space, I and II Preprint, 1996. | MR
- ,[T1] On the Euler equations of incompressible perfect fluids, J. Funct. Anal. 20 (1975), 32-43; Remarks on the Euler equations, in Proc. of "Symposia in Pure Mathematics", F. Browder ed., AMS, Providence, vol. 45 (1986), 429-430.
,[T2] Local existence of C∞ solutions of the Euler equations of incompressible perfect fluids, in Proc. Conf. on "Turbulence and Navier-Stokes", Lecture Notes in Mathematics 565 Springer-Verlag, 1976. | Zbl
,[T3] Behaviour at time t = 0 of the solutions of semi-linear evolution equations, J. Diff. Equ. 17 (1982), 73-92. | MR | Zbl
,[T4] Navier-Stokes Equations and Nonlinear Functional Analysis, CBMS-NSF Regional Conference Series in "Applied Mathematics", SIAM, Philadelphia. Second edition, 1995. | MR | Zbl
,[TW1] Asymptotic analysis of the linearized Navier-Stokes equations in a channel, Differential and Integral Equations, 8 (1995), 1591-1618. | MR | Zbl
- ,[TW2] Asymptotic analysis of the linearized Navier-Stokes equations in a general 2D domain, Asymptotic Analysis 9 (1996), 1-30. | MR | Zbl
- ,[TW3] Asymptotic analysis of Oseen type equations in a channel at small viscosity, Indiana Univ. Math. J. 45 (1996), 863-916. | MR | Zbl
- ,[TW4] Boundary layers for Oseen's type equation in space dimension three, dedicated to M. Vishik, Russian Journal of Mathematical Physics, to appear. | Zbl
- ,[TW5] The convergence of the solutions of the Navier-Stokes equations to that of the Euler equations, Applied. Math. Letters, to appear. | MR | Zbl
- ,[Vd] Perturbation Methods in Fluid Mechanics ", Academic Press, New-York. | MR | Zbl
, "[VL] Regular degeneration and boundary layer for linear differential equations with small parameter, Uspekki Mat. Nauk 12 (1957), 3-122. | MR | Zbl
- ,[Wo] Un théorème sur l'existence du mouvement plan d'un fluide parfait homogène incompressible, pendant un temps infiniment long, Math. Z. 39 (1933), 698-726. | JFM | MR | Zbl
,[YX] Singular perturbation of Euler equations with characteristic boundary condition, in preparation.
- ,