Limite incompressible des équations d’Euler non isentropiques
Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" (2000-2001), Talk no. 10, 15 p.
Métivier, Guy 1; Schochet, Steven 2

1 Université de Rennes I
2 Tel Aviv University
@article{SEDP_2000-2001____A10_0,
     author = {M\'etivier, Guy and Schochet, Steven},
     title = {Limite incompressible des \'equations {d{\textquoteright}Euler} non isentropiques},
     journal = {S\'eminaire \'Equations aux d\'eriv\'ees partielles (Polytechnique) dit aussi "S\'eminaire Goulaouic-Schwartz"},
     note = {talk:10},
     pages = {1--15},
     publisher = {Centre de math\'ematiques Laurent Schwartz, \'Ecole polytechnique},
     year = {2000-2001},
     zbl = {1061.76074},
     language = {fr},
     url = {http://archive.numdam.org/item/SEDP_2000-2001____A10_0/}
}
TY  - JOUR
AU  - Métivier, Guy
AU  - Schochet, Steven
TI  - Limite incompressible des équations d’Euler non isentropiques
JO  - Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz"
N1  - talk:10
PY  - 2000-2001
SP  - 1
EP  - 15
PB  - Centre de mathématiques Laurent Schwartz, École polytechnique
UR  - http://archive.numdam.org/item/SEDP_2000-2001____A10_0/
LA  - fr
ID  - SEDP_2000-2001____A10_0
ER  - 
%0 Journal Article
%A Métivier, Guy
%A Schochet, Steven
%T Limite incompressible des équations d’Euler non isentropiques
%J Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz"
%Z talk:10
%D 2000-2001
%P 1-15
%I Centre de mathématiques Laurent Schwartz, École polytechnique
%U http://archive.numdam.org/item/SEDP_2000-2001____A10_0/
%G fr
%F SEDP_2000-2001____A10_0
Métivier, Guy; Schochet, Steven. Limite incompressible des équations d’Euler non isentropiques. Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" (2000-2001), Talk no. 10, 15 p. http://archive.numdam.org/item/SEDP_2000-2001____A10_0/

[Ano] Anosov, Oscillations in systems of O.D.E. with rapidly oscillating solutions. Izvestia Akad.Nauk SSSR Mathematics, 24 (1960), 721–742. | MR | Zbl

[Asa] K. Asano, On the incompressible limit of the compressible Euler equation. Japan J. Appl. Math. 4 (1987), 455–488. | MR | Zbl

[Gér] P. Gérard, Microlocal defect measures. Comm. Partial Diff. Equ., 16 (1991) 1761–1794. | MR | Zbl

[Hag] G.Hagedorn, Proof of the Landau-Zener Formula in an Adiabatic Limit with Small Eigenvalue Gap. Comm. in Math. Phys., 136 (1991), 433–449. | MR | Zbl

[Hör] L. Hörmander, The Analysis of Linear Partial Differential Operators. Springer-Verlag, 1983.

[Igu] T. Iguchi, The incompressible limit and the initial layer of the compressible Euler equation in R + n . Math. Methods Appl. Sci. 20 (1997), 945–958. | MR | Zbl

[Iso1] H. Isozaki, Wave operators and the incompressible limit of the compressible Euler equation. Comm. Math. Phys. 110 (1987), 519–524. | MR | Zbl

[Iso2] H. Isozaki, Singular limits for the compressible Euler equation in an exterior domain. J. Reine Angew. Math. 381 (1987), 1–36. | MR | Zbl

[Iso3] H, Isozaki, Singular limits for the compressible Euler equation in an exterior domain. II. Bodies in a uniform flow. Osaka J. Math. 26 (1989), 399–410. | MR | Zbl

[JMR] J.L. Joly, G. Métivier et J. Rauch, Coherent and focusing multidimensional nonlinear geometric optics. Ann.Scient.E.N.S Paris, 28 (1995), 51–113. | Numdam | MR | Zbl

[Joy] Joye, Proof of the Landau-Zener Formula. Asymptotic Analysis, 9 (1994), 209–258. | MR | Zbl

[Kat] T.Kato, Perturbation Theory for Linear Operators. Springer Verlag, 1980. | Zbl

[KM1] S. Klainerman et A. Majda, Singular perturbations of quasilinear hyperbolic systems with large parameters and the incompressible limit of compressible fluids. Comm. Pure Appl. Math. 34 (1981) 481–524. | MR | Zbl

[KM2] S. Klainerman et A. Majda, Compressible and incompressible fluids. Comm. Pure Appl. Math. 35 (1982) 629–653. | MR | Zbl

[LP] P.Lax et R.Phillips, Scattering Theory. Pure and Applied Mathematics 26, Academic Press, 1989. | MR | Zbl

[LM] Lochack et Meunier, Multiphase Averaging for Classical Systems. Applied Math. Sciences 72, Springer Verlag, 1988. | MR | Zbl

[MS] G.Métivier et S.Schochet, The incompressible Limit of the Nonisentropic Euler Equations. Arch. Rat. Mech. Anal., à paraître. | Zbl

[Nei] Neischadt, Averaging in multi-frequency systems. Doklady Akad. Nauk SSSR Mechanics, 226 (1975) 314–317, Soviet Phys. Doklady, 21 (1975) 492–494. | Zbl

[RS] M. Reed et B. Simon, Methods of Modern Mathematical Physics, New York, Academic Press.

[Sch1] S. Schochet, The compressible Euler equations in a bounded domain : existence of solutions and the incompressible limit. Commun. Math. Phys. 104 (1986), 49–75. | MR | Zbl

[Sch2] S. Schochet, Asymptotics for symmetric hyperbolic systems with a large parameter. J. Diff. Eq. 75 (1988), 1–27. | MR | Zbl

[Sch3] S. Schochet, Fast singular limits of hyperbolic PDEs. J. Differential Equations 114 (1994), 476–512. | MR | Zbl

[Uhl] K.Uhlenbeck, Generic Properties of Eigenfunctions. Amer.J. Maths., 98 (1176), pp 1059-1078. | MR | Zbl

[Uka] S. Ukai, The incompressible limit and the initial layer of the compressible Euler equation. J. Math. Kyoto Univ. 26 (1986), 323–331. | MR | Zbl