On the behavior of the solutions of the Navier-Stokes equations at vanishing viscosity
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 4, Volume 25 (1997) no. 3-4, p. 807-828 
@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},
     publisher = {Scuola normale superiore},
     volume = {Ser. 4, 25},
     number = {3-4},
     year = {1997},
     pages = {807-828},
     zbl = {1043.35127},
     mrnumber = {1655543},
     language = {en},
     url = {http://www.numdam.org/item/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, Serie 4, Volume 25 (1997) no. 3-4, pp. 807-828. http://www.numdam.org/item/ASNSP_1997_4_25_3-4_807_0/

[Al] S.N. Alekseenko, 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 1288259 | Zbl 0856.35099

[As] K. Asano, Zero-Viscosity Limit of the Incompressible Navier-Stokes Equations 1, 2, Preprint, University of Kyoto, 1997.

[BP] R. Balian - J.L. Peube, "Fluid Dynamics", Cours de l'Ecole d'Ete de Physique Théorique, Les Houches Gordon and Breach Science Publishers, New-York, 1977. | MR 495783 | Zbl 0348.00025

[BC1] G.I. Barenblatt - A.J. Chorin, 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 0856.76026

[BC2] G.I. Barenblatt - A.J. Chorin, 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 1492690

[Ba] G.K. Batchelor, "An Introduction to Fluid Dynamics", Cambridge University Press, Cambridge, 1967. | MR 1744638 | Zbl 0152.44402

[BKM] J.T. Beale - T. Kato - A. Majda, Remarks on the breakdown of smooth solutions for the 3D Euler equations, Comm. Math. Phys. 94 (1984), 61-66. | MR 763762 | Zbl 0573.76029

[Ch] A.J. Chorin, Turbulence as a near-equilibrium process, in Lecture in Applied Mathematics 31 (1996), 235-249, AMS, Providence. | MR 1363031 | Zbl 0838.76034

[CW] P. Constantin - J. Wu, Inviscid limit for vortex patches, Nonlinearity 8 (1995), 735-742. | MR 1355040 | Zbl 0832.76011

[EE] Weinan E. - B. Engquist, Blow-up of Solutions of the Unsteady Prandtl's Equation, preprint, 1996.

[EM] D.G. Ebin - J. Marsden, Groups of diffeomorphisms and the motion of an incompressible fluid, Arch. Rational Mech. Anal. 46 (1972), 241-279. | MR 426034

[E] W. Eckhaus, "Asymptotic Analysis of Singular Perturbations ", North-Holland, 1979. | MR 553107 | Zbl 0421.34057

[F] P. Fife, Considerations regarding the mathematical basis for Prandtl's boundary layer theory, Arch. Rational Mech. Anal. 38 (1967), 184-216. | MR 227633 | Zbl 0172.53801

[Ge] P. Germain, "Méthodes Asymptotiques en Mécanique des Fluides ", in [BP]. | Zbl 0387.76001

[Gr] H.P. Greenspan, "The Theory of Rotating Fluids", Cambridge Univ. Press, Cambridge, 1968. | MR 639897 | Zbl 0182.28103

[K1] K. Kato, "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 765230

[K2] T. Kato, On the classical solutions of two dimensional nonstationary Euler equations, Arch. Rational Mech. Anal 25 (1967), 188-200. | MR 211057 | Zbl 0166.45302

[La] P. Lagerström, "Matched Asymptotics Expansion, Ideas and Techniques ", Springer-Verlag, New-York, 1988. | MR 958913 | Zbl 0666.34064

[LL] L. Landau - E. Lifschitz, "Fluid Mechanics", Addison-Wesley, New-York, 1953.

[Lc] L. Lichtenstein, "Grundlagen der Hydromechanik", Springer-Verlag, 1923. | JFM 55.1124.01 | MR 228225 | Zbl 0157.56701

[Lo1] J.L. Lions, "Quelques Méthodes de Résolution des Problèmes aux Limites non Linéaires ", Dunod, Paris, 1969. | MR 259693 | Zbl 0189.40603

[Lo2] J.L. Lions, Perturbations singulières dans les problèmes aux limites et en contrôle optimal, Lecture Notes in Math. 323 Springer-Verlag, New-York, 1973. | MR 600331 | Zbl 0268.49001

[M] A. Majda, "Compressible fluid flow and systems of conservation laws in several space variables", Springer-Verlag, New-York, 1984. | MR 748308 | Zbl 0537.76001

[O] O. Oleinik, The Prandtl system of equations in boundary layer theory, Dokl. Akad. Nauk S.S.S.R. 150, 4(3) (1963), 583-586. | Zbl 0134.45004

[Pr] L. Prandtl, Veber Flüssigkeiten bei sehr kleiner Reibung, Verh. III Intern. Math. Kongr. Heidelberg (1905), 484-491, Teuber, Leibzig. | JFM 36.0800.02

[SC] M. Sammartino - R.E. Caflish, Zero viscosity limit for analytic solutions of the Navier-Stokes equation on a half-space, I and II Preprint, 1996. | MR 1461106

[T1] R. Temam, 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] R. Temam, 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 0355.76017

[T3] R. Temam, Behaviour at time t = 0 of the solutions of semi-linear evolution equations, J. Diff. Equ. 17 (1982), 73-92. | MR 645638 | Zbl 0446.35057

[T4] R. Temam, Navier-Stokes Equations and Nonlinear Functional Analysis, CBMS-NSF Regional Conference Series in "Applied Mathematics", SIAM, Philadelphia. Second edition, 1995. | MR 1318914 | Zbl 0833.35110

[TW1] R. Temam - X. Wang, Asymptotic analysis of the linearized Navier-Stokes equations in a channel, Differential and Integral Equations, 8 (1995), 1591-1618. | MR 1347972 | Zbl 0832.35112

[TW2] R. Temam - X. Wang, Asymptotic analysis of the linearized Navier-Stokes equations in a general 2D domain, Asymptotic Analysis 9 (1996), 1-30. | MR 1383673 | Zbl 0889.35076

[TW3] R. Temam - X. Wang, Asymptotic analysis of Oseen type equations in a channel at small viscosity, Indiana Univ. Math. J. 45 (1996), 863-916. | MR 1422110 | Zbl 0881.35097

[TW4] R. Temam - X. Wang, Boundary layers for Oseen's type equation in space dimension three, dedicated to M. Vishik, Russian Journal of Mathematical Physics, to appear. | Zbl 0912.35125

[TW5] R. Temam - X. Wang, The convergence of the solutions of the Navier-Stokes equations to that of the Euler equations, Applied. Math. Letters, to appear. | MR 1471313 | Zbl 0888.35077

[Vd] M. Van Dyke, "Perturbation Methods in Fluid Mechanics ", Academic Press, New-York. | MR 416240 | Zbl 0136.45001

[VL] M.I. Vishik - L.A. Lyusternik, Regular degeneration and boundary layer for linear differential equations with small parameter, Uspekki Mat. Nauk 12 (1957), 3-122. | MR 96041 | Zbl 0087.29602

[Wo] W. Wolibner, 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 59.1447.02 | MR 1545430 | Zbl 0008.06901

[YX] T. Yanagisawa - Z. Xin, Singular perturbation of Euler equations with characteristic boundary condition, in preparation.