Alentours de la limite incompressible

 Access to full text

 Full (PDF)

1. T. Alazard, Incompressible limit of the nonisentropic Euler equations with solid wall boundary conditions, Adv. in Differential Equations10, 19–44 (2005). Zbl1101.35050MR2106119
2. T. Alazard, Low Mach number limit of the full Navier–Stokes equations, Arch. Ration. Mech. Anal, accepté. Zbl1108.76061MR2211706
3. T. Alazard, Low Mach number limit of the full Navier–Stokes equations II, en cours. Zbl1108.76061
4. S. Benzoni-Gavage, R. Danchin & S. Descombes, Well-posedness of one-dimensional Korteweg models, prépublication. Zbl1114.76058
5. D. Bresch & B. Desjardins, Existence of global weak solutions to the Navier-Stokes equations for viscous compressible and heat conducting fluids. Zbl1122.35092
6. D. Bresch, B. Desjardins & D. Gerard–Varet, Rotating Fluids in a cylinder, Disc. Cont. Dyn. Sys.- Series A 1, 47–82 (2004). Zbl1138.76446MR2073946
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). Zbl1114.76347MR1917042
8. D. Bresch, D. Gerard-Varet & E. Grenier, Derivation of the planetary geostrophic equations, prépublication. Zbl1104.76081
9. C. Cheverry, Propagation of oscillations in real vanishing viscosity limit, Comm. Math. Phys., 247, 655–695 (2004). Zbl1079.35060MR2062647
10. R. Danchin, Zero Mach number limit for compressible flows with periodic boundary conditions, Amer. J. Math.124, 1153–1219 (2002). Zbl1048.35075MR1939784
11. R. Danchin, Zero Mach number limit in critical spaces for compressible Navier-Stokes equations, Ann. Sci. École Norm. Sup.35, 27–75 (2002). Zbl1048.35054MR1886005
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). Zbl1018.76037MR1864120
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). Zbl1080.35067MR2157145
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). Zbl0934.76080MR1702718
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). Zbl0992.35067MR1697038
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). Zbl1059.35095MR2059677
17. I. Gallagher, A remark on smooth solutions of the weakly compressible periodic Navier–Stokes equations, J. Math. Kyoto Univ., 40 525–540 (2000). Zbl0997.35050MR1794519
18. I. Gallagher, Résultats récents sur la limite incompressible, Séminaire Bourbaki2003–2004, num. 926. Zbl1329.76292MR2167201
19. I. Gallagher & L. Saint-Raymond, On pressureless gases driven by a strong inhomogeneous magnetic field, SIAM Journal for Mathematical Analysis, accepté. Zbl1145.35095
20. E. Grenier, Oscillatory perturbations of the Navier-Stokes equations, J. Math. Pures Appl.76, 477–498 (1997). Zbl0885.35090MR1465607
21. H. Isozaki, Singular limits for the compressible Euler equation in an exterior domain, J. Reine Angew. Math.381, 1–36 (1987). Zbl0618.76073MR918838
22. H. Isozaki, Wave operators and the incompressible limit of the compressible Euler equation Comm. Math. Phys., 110, 519–524 (1987). Zbl0627.76081MR891951
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). Zbl0699.35171MR957056
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). Zbl0476.76068MR615627
25. S. Klainerman & A. Majda, Compressible and incompressible fluids, Comm. Pure Appl. Math.35, 629–651 (1982). Zbl0478.76091MR668409
26. P.-L. Lions, Mathematical topics in fluid mechanics. Vol. 1, Incompressible models, Oxford Science Publications (1996). Zbl0866.76002MR1422251
27. P.-L. Lions & N. Masmoudi, Incompressible limit for a viscous compressible fluid, J. Math. Pures Appl. (9)77, 585–627 (1998). Zbl0909.35101MR1628173
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). Zbl0937.35132MR1710123
29. A. Majda, Compressible fluid flow and systems of conservation laws in several space variables, Applied Mathematical Sciences 53, Springer-Verlag (1984). Zbl0537.76001MR748308
30. M. Majdoub & M. Paicu, Uniform local existence for inhomogenous rotating fluid equations, prépublication. Zbl1160.76052
31. G. Métivier & S. Schochet, The incompressible limit of the non-isentropic Euler equations, Arch. Ration. Mech. Anal.158, 61–90 (2001). Zbl0974.76072MR1834114
32. G. Métivier & S. Schochet, Limite incompressible des équations d’Euler non isentropiques, Séminaire : Équations aux Dérivées Partielles 2000–2001. Zbl1061.76074
33. G. Métivier & S. Schochet, Averaging theorems for conservative systems and the weakly compressible Euler equations, J. Differential Equations187, 106–183 (2003). Zbl1029.34035MR1946548
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). Zbl0612.76082MR834481
35. S. Schochet, Fast singular limits of hyperbolic PDE’s, J. Differential Equations114, 476–512 (1994). Zbl0838.35071
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). Zbl1094.35094MR2157144
37. P. Secchi, On slightly compressible ideal flow in the half-plane, Arch. Ration. Mech. Anal., 161, 231–255 (2002). Zbl1026.76040MR1894592