On the behavior of the solutions of the Navier-Stokes equations at vanishing viscosity
- [1] The Institute for Scientific Computing and Applied Mathematics, Indiana University, Bloomington, IN, USA.
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1997)
- Volume: 25, Issue: 3-4, page 807-828
- ISSN: 0391-173X
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topTemam, Roger, and 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 25.3-4 (1997): 807-828. <http://eudml.org/doc/84316>.
@article{Temam1997,
affiliation = {The Institute for Scientific Computing and Applied Mathematics, Indiana University, Bloomington, IN, USA.},
author = {Temam, Roger, Wang, Xiaoming},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {convergence; Navier-Stokes equations; Euler equations; channel; bounded domain},
language = {eng},
number = {3-4},
pages = {807-828},
publisher = {Scuola normale superiore},
title = {On the behavior of the solutions of the Navier-Stokes equations at vanishing viscosity},
url = {http://eudml.org/doc/84316},
volume = {25},
year = {1997},
}
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
PB - Scuola normale superiore
VL - 25
IS - 3-4
SP - 807
EP - 828
LA - eng
KW - convergence; Navier-Stokes equations; Euler equations; channel; bounded domain
UR - http://eudml.org/doc/84316
ER -
References
top- [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. Zbl0856.35099MR1288259
- [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 HouchesGordon and Breach Science Publishers, New-York, 1977. Zbl0348.00025MR495783
- [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 Mathematics93 (1996). Zbl0856.76026
- [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. MR1492690
- [Ba] G.K. Batchelor, "An Introduction to Fluid Dynamics", Cambridge University Press, Cambridge, 1967. Zbl0152.44402MR1744638
- [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. Zbl0573.76029MR763762
- [Ch] A.J. Chorin, Turbulence as a near-equilibrium process, in Lecture in Applied Mathematics31 (1996), 235-249, AMS, Providence. Zbl0838.76034MR1363031
- [CW] P. Constantin - J. Wu, Inviscid limit for vortex patches, Nonlinearity8 (1995), 735-742. Zbl0832.76011MR1355040
- [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. MR426034
- [E] W. Eckhaus, "Asymptotic Analysis of Singular Perturbations ", North-Holland, 1979. Zbl0421.34057MR553107
- [F] P. Fife, Considerations regarding the mathematical basis for Prandtl's boundary layer theory, Arch. Rational Mech. Anal.38 (1967), 184-216. Zbl0172.53801MR227633
- [Ge] P. Germain, "Méthodes Asymptotiques en Mécanique des Fluides ", in [BP]. Zbl0387.76001
- [Gr] H.P. Greenspan, "The Theory of Rotating Fluids", Cambridge Univ. Press, Cambridge, 1968. Zbl0182.28103MR639897
- [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. MR765230
- [K2] T. Kato, On the classical solutions of two dimensional nonstationary Euler equations, Arch. Rational Mech. Anal25 (1967), 188-200. Zbl0166.45302MR211057
- [La] P. Lagerström, "Matched Asymptotics Expansion, Ideas and Techniques ", Springer-Verlag, New-York, 1988. Zbl0666.34064MR958913
- [LL] L. Landau - E. Lifschitz, "Fluid Mechanics", Addison-Wesley, New-York, 1953.
- [Lc] L. Lichtenstein, "Grundlagen der Hydromechanik", Springer-Verlag, 1923. Zbl0157.56701MR228225JFM55.1124.01
- [Lo1] J.L. Lions, "Quelques Méthodes de Résolution des Problèmes aux Limites non Linéaires ", Dunod, Paris, 1969. Zbl0189.40603MR259693
- [Lo2] J.L. Lions, Perturbations singulières dans les problèmes aux limites et en contrôle optimal, Lecture Notes in Math. 323Springer-Verlag, New-York, 1973. Zbl0268.49001MR600331
- [M] A. Majda, "Compressible fluid flow and systems of conservation laws in several space variables", Springer-Verlag, New-York, 1984. Zbl0537.76001MR748308
- [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. Zbl0134.45004
- [Pr] L. Prandtl, Veber Flüssigkeiten bei sehr kleiner Reibung, Verh. III Intern. Math. Kongr. Heidelberg (1905), 484-491, Teuber, Leibzig. JFM36.0800.02
- [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. MR1461106
- [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. Zbl0309.35061
- [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 565Springer-Verlag, 1976. Zbl0355.76017
- [T3] R. Temam, Behaviour at time t = 0 of the solutions of semi-linear evolution equations, J. Diff. Equ.17 (1982), 73-92. Zbl0446.35057MR645638
- [T4] R. Temam, Navier-Stokes Equations and Nonlinear Functional Analysis, CBMS-NSF Regional Conference Series in "Applied Mathematics", SIAM, Philadelphia. Second edition, 1995. Zbl0833.35110MR1318914
- [TW1] R. Temam - X. Wang, Asymptotic analysis of the linearized Navier-Stokes equations in a channel, Differential and Integral Equations, 8 (1995), 1591-1618. Zbl0832.35112MR1347972
- [TW2] R. Temam - X. Wang, Asymptotic analysis of the linearized Navier-Stokes equations in a general 2D domain, Asymptotic Analysis9 (1996), 1-30. Zbl0889.35076MR1383673
- [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. Zbl0881.35097MR1422110
- [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. Zbl0912.35125
- [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. Zbl0888.35077MR1471313
- [Vd] M. Van Dyke, "Perturbation Methods in Fluid Mechanics ", Academic Press, New-York. Zbl0136.45001MR416240
- [VL] M.I. Vishik - L.A. Lyusternik, Regular degeneration and boundary layer for linear differential equations with small parameter, Uspekki Mat. Nauk12 (1957), 3-122. Zbl0087.29602MR96041
- [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. Zbl0008.06901MR1545430JFM59.1447.02
- [YX] T. Yanagisawa - Z. Xin, Singular perturbation of Euler equations with characteristic boundary condition, in preparation.
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