Alentours de la limite incompressible
Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" (2004-2005), Talk no. 23, 16 p.

Le résultat principal de cet exposé énonce que le problème de Cauchy pour les équations adimensionnées d’un fluide général est bien posé sur un intervalle de temps indépendant des nombres de Mach, Reynolds et Péclet.

Alazard, Thomas 1

1 MAB, Université de Bordeaux I, 33405 Talence
@article{SEDP_2004-2005____A23_0,
     author = {Alazard, Thomas},
     title = {Alentours de la limite incompressible},
     journal = {S\'eminaire \'Equations aux d\'eriv\'ees partielles (Polytechnique) dit aussi "S\'eminaire Goulaouic-Schwartz"},
     note = {talk:23},
     publisher = {Centre de math\'ematiques Laurent Schwartz, \'Ecole polytechnique},
     year = {2004-2005},
     mrnumber = {2182067},
     language = {fr},
     url = {http://archive.numdam.org/item/SEDP_2004-2005____A23_0/}
}
TY  - JOUR
AU  - Alazard, Thomas
TI  - Alentours de la limite incompressible
JO  - Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz"
N1  - talk:23
PY  - 2004-2005
DA  - 2004-2005///
PB  - Centre de mathématiques Laurent Schwartz, École polytechnique
UR  - http://archive.numdam.org/item/SEDP_2004-2005____A23_0/
UR  - https://www.ams.org/mathscinet-getitem?mr=2182067
LA  - fr
ID  - SEDP_2004-2005____A23_0
ER  - 
%0 Journal Article
%A Alazard, Thomas
%T Alentours de la limite incompressible
%J Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz"
%Z talk:23
%D 2004-2005
%I Centre de mathématiques Laurent Schwartz, École polytechnique
%G fr
%F SEDP_2004-2005____A23_0
Alazard, Thomas. Alentours de la limite incompressible. Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" (2004-2005), Talk no. 23, 16 p. http://archive.numdam.org/item/SEDP_2004-2005____A23_0/

[1] T. Alazard, Incompressible limit of the nonisentropic Euler equations with solid wall boundary conditions, Adv. in Differential Equations 10, 19–44 (2005). | MR | Zbl

[2] T. Alazard, Low Mach number limit of the full Navier–Stokes equations, Arch. Ration. Mech. Anal, accepté. | MR | Zbl

[3] T. Alazard, Low Mach number limit of the full Navier–Stokes equations II, en cours.

[4] S. Benzoni-Gavage, R. Danchin & S. Descombes, Well-posedness of one-dimensional Korteweg models, prépublication. | Zbl

[5] D. Bresch & B. Desjardins, Existence of global weak solutions to the Navier-Stokes equations for viscous compressible and heat conducting fluids. | Zbl

[6] D. Bresch, B. Desjardins & D. Gerard–Varet, Rotating Fluids in a cylinder, Disc. Cont. Dyn. Sys.- Series A 1, 47–82 (2004). | MR | Zbl

[7] D. Bresch, B. Desjardins, E. Grenier & C.-K. Lin, Low Mach number limit of viscous polytropic flows : formal asymptotics in the periodic case, Stud. Appl. Math. 109, 125–149 (2002). | MR | Zbl

[8] D. Bresch, D. Gerard-Varet & E. Grenier, Derivation of the planetary geostrophic equations, prépublication. | Zbl

[9] C. Cheverry, Propagation of oscillations in real vanishing viscosity limit, Comm. Math. Phys., 247, 655–695 (2004). | MR | Zbl

[10] R. Danchin, Zero Mach number limit for compressible flows with periodic boundary conditions, Amer. J. Math. 124, 1153–1219 (2002). | MR | Zbl

[11] R. Danchin, Zero Mach number limit in critical spaces for compressible Navier-Stokes equations, Ann. Sci. École Norm. Sup. 35, 27–75 (2002). | Numdam | MR | Zbl

[12] R. Danchin, Global existence in critical spaces for flows of compressible viscous and heat-conductive gases, Arch. Ration. Mech. Anal., 160, 1–39 (2001). | MR | Zbl

[13] R. Danchin, Low Mach number limit for viscous compressible flows, M2AN Math. Model. Numer. Anal. specail issue ol. 39 No. 3 (May-June 2005). | Numdam | MR | Zbl

[14] B. Desjardins & E. Grenier, Low Mach number limit of viscous compressible flows in the whole space, R. Soc. Lond. Proc. Ser. A Math. Phys. Eng. Sci. 455, 2271–2279 (1999). | MR | Zbl

[15] B. Desjardins, E. Grenier, P.-L. Lions & N. Masmoudi, Incompressible limit for solutions of the isentropic Navier-Stokes equations with Dirichlet boundary conditions, J. Math. Pures Appl. 78, 461–471 (1999). | MR | Zbl

[16] A. Dutrifoy & T. Hmidi, The incompressible limit of solutions of the two-dimensional compressible Euler system with degenerating initial data, Comm. Pure Appl. Math., 57 1159–1177 (2004). | MR | Zbl

[17] I. Gallagher, A remark on smooth solutions of the weakly compressible periodic Navier–Stokes equations, J. Math. Kyoto Univ., 40 525–540 (2000). | MR | Zbl

[18] I. Gallagher, Résultats récents sur la limite incompressible, Séminaire Bourbaki 2003–2004, num. 926. | Numdam | MR | Zbl

[19] I. Gallagher & L. Saint-Raymond, On pressureless gases driven by a strong inhomogeneous magnetic field, SIAM Journal for Mathematical Analysis, accepté. | Zbl

[20] E. Grenier, Oscillatory perturbations of the Navier-Stokes equations, J. Math. Pures Appl. 76, 477–498 (1997). | MR | Zbl

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

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

[23] S. Kawashima & Y. Shizuta, On the normal form of the symmetric hyperbolic-parabolic systems associated with the conservation laws, Tohoku Math. J. 40 449–464 (1988). | MR | Zbl

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

[25] S. Klainerman & A. Majda, Compressible and incompressible fluids, Comm. Pure Appl. Math. 35, 629–651 (1982). | MR | Zbl

[26] P.-L. Lions, Mathematical topics in fluid mechanics. Vol. 1, Incompressible models, Oxford Science Publications (1996). | MR | Zbl

[27] P.-L. Lions & N. Masmoudi, Incompressible limit for a viscous compressible fluid, J. Math. Pures Appl. (9) 77, 585–627 (1998). | MR | Zbl

[28] P.-L. Lions & N. Masmoudi, Une approche locale de la limite incompressible, C. R. Acad. Sci. Paris Sér. I Math. 329, 387–392 (1999). | MR | Zbl

[29] A. Majda, Compressible fluid flow and systems of conservation laws in several space variables, Applied Mathematical Sciences 53, Springer-Verlag (1984). | MR | Zbl

[30] M. Majdoub & M. Paicu, Uniform local existence for inhomogenous rotating fluid equations, prépublication.

[31] G. Métivier & S. Schochet, The incompressible limit of the non-isentropic Euler equations, Arch. Ration. Mech. Anal. 158, 61–90 (2001). | MR | Zbl

[32] G. Métivier & S. Schochet, Limite incompressible des équations d’Euler non isentropiques, Séminaire : Équations aux Dérivées Partielles 2000–2001. | Numdam | Zbl

[33] G. Métivier & S. Schochet, Averaging theorems for conservative systems and the weakly compressible Euler equations, J. Differential Equations 187, 106–183 (2003). | MR | Zbl

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

[35] S. Schochet, Fast singular limits of hyperbolic PDE’s, J. Differential Equations 114, 476–512 (1994). | Zbl

[36] S. Schochet, The mathematical theory of low Mach numbers flows, M2AN Math. Model. Numer. Anal. specail issue ol. 39 No. 3 (May-June 2005). | Numdam | MR | Zbl

[37] P. Secchi, On slightly compressible ideal flow in the half-plane, Arch. Ration. Mech. Anal., 161, 231–255 (2002). | MR | Zbl