Zero Mach number limit in critical spaces for compressible Navier–Stokes equations

 Access to full text

 Full (PDF)

1. [1] Bony J.-M., Calcul symbolique et propagation des singularités pour les équations aux dérivées partielles non linéaires, Ann. Sci. École Norm. Sup.14 (1981) 209-246. Zbl0495.35024MR631751
2. [2] Cannone M., Ondelettes, paraproduits et Navier–Stokes, Nouveaux essais, Diderot éditeurs, 1995. Zbl1049.35517MR1688096
3. [3] Chemin J.-Y., Remarques sur l'existence globale pour le système de Navier–Stokes incompressible, SIAM J. Math. Anal.23 (1992) 20-28. Zbl0762.35063MR1145160
4. [4] Chemin J.-Y., About Navier–Stokes system, Prépublication du Laboratoire d'analyse numérique de Paris 6, R96023, 1996. 
5. [5] Chemin J.-Y., Théorèmes d'unicité pour le système de Navier–Stokes tridimensionnel, J. Anal. Math.77 (1999) 27-50. Zbl0938.35125MR1753481
6. [6] Danchin R., Global existence in critical spaces for compressible Navier–Stokes equations, Inventiones Math.141 (2000) 579-614. Zbl0958.35100MR1779621
7. [7] Danchin R., Local theory in critical spaces for compressible viscous and heat-conductive gases, Comm. Partial Differential Equations26 (2001) 1183-1233. Zbl1007.35071MR1855277
8. [8] Danchin R., Global existence in critical spaces for compressible viscous and heat-conductive gases, Arch. Rational Mech. Anal.160 (2001) 1-39. Zbl1018.76037MR1864120
9. [9] Danchin R., Zero Mach number limit for compressible flows with periodic boundary conditions, submitted. Zbl1048.35075
10. [10] Danchin R., On the uniquiness in critical spaces for compressible Navier–Stokes equations, Nonlinear Differential Equations Appl., to appear. Zbl1125.76061MR2138937
11. [11] Desjardins B., Grenier E., Low Mach number limit of viscous compressible flows in the whole space, Roy. Soc. London Proc. Series A455 (1986) (1999) 2271-2279. Zbl0934.76080MR1702718
12. [12] Desjardins B., Grenier E., Lions P.-L., Masmoudi N., Incompressible limit for solutions of the isentropic Navier–Stokes equations with Dirichlet boundary conditions, J. Math. Pures Appl.78 (1999) 461-471. Zbl0992.35067MR1697038
13. [13] Fabrie P., Galusinski C., The slightly compressible Navier–Stokes equations revisited, Preprint, Mathématiques Appliquées de Bordeaux, France, 1998. Zbl1027.35092MR1868354
14. [14] Fujita H., Kato T., On the Navier–Stokes initial value problem I, Arch. Rational Mech. Anal.16 (1964) 269-315. Zbl0126.42301MR166499
15. [15] Gallagher I., A remark on smooth solutions of the weakly compressible periodic Navier–Stokes equations, Prépublication Université Paris-Sud, Mathématiques, 1999. MR1794519
16. [16] Ginibre J., Velo G., Generalized Strichartz inequalities for the wave equation, J. Funct. Anal.133 (1995) 50-68. Zbl0849.35064MR1351643
17. [17] Hagstrom T., Lorenz J., All-time existence of classical solutions for slightly compressible flows, SIAM J. Math. Anal.29 (1998) 652-672. Zbl0907.76073MR1617767
18. [18] Hoff D., The zero-Mach limit of compressible flows, Comm. Math. Phys.192 (1998) 543-554. Zbl0907.35098MR1620511
19. [19] Hoff D., Zumbrun K., Multi-dimensional diffusion waves for the Navier–Stokes equations of compressible flow, Indiana Univ. Math. J.44 (1995) 603-676. Zbl0842.35076MR1355414
20. [20] Keel M., Tao T., Endpoint Strichartz estimates, Amer. J. Math.120 (1998) 955-980. Zbl0922.35028MR1646048
21. [21] Klainerman S., Majda A., Compressible and incompressible fluids, Comm. Pure Appl. Math.35 (1982) 629-651. Zbl0478.76091MR668409
22. [22] Kreiss H.-O., Lorenz J., Naughton M., Convergence of the solutions of the compressible to the solutions of the incompressible Navier–Stokes equations, Adv. Pure Appl. Math.12 (1991) 187-214. Zbl0728.76084MR1101207
23. [23] Leray J., Sur le mouvement d'un liquide visqueux remplissant l'espace, Acta Math.63 (1934) 193-248. MR1555394JFM60.0726.05
24. [24] Lin C., On the incompressible limit of the compressible Navier–Stokes equations, Comm. Partial Differential Equations20 (1995) 677-707. Zbl0816.35105MR1318085
25. [25] Lions P.-L., Mathematical Topics in Fluid Dynamics, Vol. 1. Incompressible Models, Oxford University Press, 1996. Zbl0866.76002MR1422251
26. [26] Lions P.-L., Mathematical Topics in Fluid Dynamics, Vol. 2. Compressible Models, Oxford University Press, 1998. Zbl0908.76004MR1637634
27. [27] Lions P.-L., Masmoudi N., Incompressible limit for a viscous compressible fluid, J. Math. Pures Appl.77 (1998) 585-627. Zbl0909.35101MR1628173
28. [28] Lions P.-L., Masmoudi N., Une approche locale de la limite incompressible, C. R. Acad. Sci. Paris, Série I329 (1999) 387-392. Zbl0937.35132MR1710123
29. [29] Peetre J., New Thoughts on Besov Spaces, Duke University Mathematical Series, Vol. 1, Durham N.C., 1976. Zbl0356.46038MR461123
30. [30] Runst T., Sickel W., Sobolev Spaces of Fractional Order, Nemytskij Operators, and Nonlinear Partial Differential Equations, de Gruyter Series in Nonlinear Analysis and Applications, 3, Walter de Gruyter, Berlin, 1996. Zbl0873.35001MR1419319
31. [31] Strichartz R., Restriction of Fourier transform to quadratic surfaces and decay of solutions of wave equations, Duke Math. J.44 (1977) 705-774. Zbl0372.35001MR512086
32. [32] Ukai S., The incompressible limit and the initial layer of the compressible Euler equation, J. Math. Kyoto Univ.26 (1986) 323-331. Zbl0618.76074MR849223

1. Alexandre Dutrifoy, Limite incompressible de solutions du système d’Euler compressible 2-D dans certains cas mal préparés
2. Raphaël Danchin, Bernard Ducomet, Résultats d’existence globale et limites asymptotiques pour un modèle de fluide radiatif
3. Raphaël Danchin, Fluides légèrement compressibles et limite incompressible
4. Raphaël Danchin, Low Mach number limit for viscous compressible flows
5. Raphaël Danchin, Low Mach number limit for viscous compressible flows
6. Thomas Alazard, Alentours de la limite incompressible
7. Isabelle Gallagher, Résultats récents sur la limite incompressible