Zero Mach number limit in critical spaces for compressible Navier-Stokes equations
Danchin, Raphaël
Annales scientifiques de l'École Normale Supérieure, Tome 35 (2002), p. 27-75 / Harvested from Numdam
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@article{ASENS_2002_4_35_1_27_0,
     author = {Danchin, Rapha\"el},
     title = {Zero Mach number limit in critical spaces for compressible Navier-Stokes equations},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     volume = {35},
     year = {2002},
     pages = {27-75},
     doi = {10.1016/s0012-9593(01)01085-0},
     zbl = {1048.35054},
     language = {en},
     url = {http://dml.mathdoc.fr/item/ASENS_2002_4_35_1_27_0}
}

Danchin, Raphaël. Zero Mach number limit in critical spaces for compressible Navier-Stokes equations. Annales scientifiques de l'École Normale Supérieure, Tome 35 (2002) pp. 27-75. doi : 10.1016/s0012-9593(01)01085-0. http://gdmltest.u-ga.fr/item/ASENS_2002_4_35_1_27_0/

[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. | Numdam | MR 631751 | Zbl 0495.35024

[2] Cannone M., Ondelettes, paraproduits et Navier-Stokes, Nouveaux essais, Diderot éditeurs, 1995. | MR 1688096 | Zbl 1049.35517

[3] Chemin J.-Y., Remarques sur l'existence globale pour le système de Navier-Stokes incompressible, SIAM J. Math. Anal. 23 (1992) 20-28. | MR 1145160 | Zbl 0762.35063

[4] Chemin J.-Y., About Navier-Stokes system, Prépublication du Laboratoire d'analyse numérique de Paris 6, R96023, 1996.

[5] Chemin J.-Y., Théorèmes d'unicité pour le système de Navier-Stokes tridimensionnel, J. Anal. Math. 77 (1999) 27-50. | MR 1753481 | Zbl 0938.35125

[6] Danchin R., Global existence in critical spaces for compressible Navier-Stokes equations, Inventiones Math. 141 (2000) 579-614. | MR 1779621 | Zbl 0958.35100

[7] Danchin R., Local theory in critical spaces for compressible viscous and heat-conductive gases, Comm. Partial Differential Equations 26 (2001) 1183-1233. | MR 1855277 | Zbl 1007.35071

[8] Danchin R., Global existence in critical spaces for compressible viscous and heat-conductive gases, Arch. Rational Mech. Anal. 160 (2001) 1-39. | MR 1864120 | Zbl 1018.76037

[9] Danchin R., Zero Mach number limit for compressible flows with periodic boundary conditions, submitted. | Zbl 1048.35075

[10] Danchin R., On the uniquiness in critical spaces for compressible Navier-Stokes equations, Nonlinear Differential Equations Appl., to appear. | MR 2138937 | Zbl 02193888

[11] Desjardins B., Grenier E., Low Mach number limit of viscous compressible flows in the whole space, Roy. Soc. London Proc. Series A 455 (1986) (1999) 2271-2279. | MR 1702718 | Zbl 0934.76080

[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. | MR 1697038 | Zbl 0992.35067

[13] Fabrie P., Galusinski C., The slightly compressible Navier-Stokes equations revisited, Preprint, Mathématiques Appliquées de Bordeaux, France, 1998. | MR 1868354

[14] Fujita H., Kato T., On the Navier-Stokes initial value problem I, Arch. Rational Mech. Anal. 16 (1964) 269-315. | MR 166499 | Zbl 0126.42301

[15] Gallagher I., A remark on smooth solutions of the weakly compressible periodic Navier-Stokes equations, Prépublication Université Paris-Sud, Mathématiques, 1999. | MR 1794519

[16] Ginibre J., Velo G., Generalized Strichartz inequalities for the wave equation, J. Funct. Anal. 133 (1995) 50-68. | MR 1351643 | Zbl 0849.35064

[17] Hagstrom T., Lorenz J., All-time existence of classical solutions for slightly compressible flows, SIAM J. Math. Anal. 29 (1998) 652-672. | MR 1617767 | Zbl 0907.76073

[18] Hoff D., The zero-Mach limit of compressible flows, Comm. Math. Phys. 192 (1998) 543-554. | MR 1620511 | Zbl 0907.35098

[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. | MR 1355414 | Zbl 0842.35076

[20] Keel M., Tao T., Endpoint Strichartz estimates, Amer. J. Math. 120 (1998) 955-980. | MR 1646048 | Zbl 0922.35028

[21] Klainerman S., Majda A., Compressible and incompressible fluids, Comm. Pure Appl. Math. 35 (1982) 629-651. | MR 668409 | Zbl 0478.76091

[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. | MR 1101207 | Zbl 0728.76084

[23] Leray J., Sur le mouvement d'un liquide visqueux remplissant l'espace, Acta Math. 63 (1934) 193-248. | JFM 60.0726.05 | MR 1555394

[24] Lin C., On the incompressible limit of the compressible Navier-Stokes equations, Comm. Partial Differential Equations 20 (1995) 677-707. | MR 1318085 | Zbl 0816.35105

[25] Lions P.-L., Mathematical Topics in Fluid Dynamics, Vol. 1. Incompressible Models, Oxford University Press, 1996. | MR 1422251 | Zbl 0866.76002

[26] Lions P.-L., Mathematical Topics in Fluid Dynamics, Vol. 2. Compressible Models, Oxford University Press, 1998. | MR 1637634 | Zbl 0908.76004

[27] Lions P.-L., Masmoudi N., Incompressible limit for a viscous compressible fluid, J. Math. Pures Appl. 77 (1998) 585-627. | MR 1628173 | Zbl 0909.35101

[28] Lions P.-L., Masmoudi N., Une approche locale de la limite incompressible, C. R. Acad. Sci. Paris, Série I 329 (1999) 387-392. | MR 1710123 | Zbl 0937.35132

[29] Peetre J., New Thoughts on Besov Spaces, Duke University Mathematical Series, Vol. 1, Durham N.C., 1976. | MR 461123 | Zbl 0356.46038

[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. | MR 1419319 | Zbl 0873.35001

[31] Strichartz R., Restriction of Fourier transform to quadratic surfaces and decay of solutions of wave equations, Duke Math. J. 44 (1977) 705-774. | MR 512086 | Zbl 0372.35001

[32] Ukai S., The incompressible limit and the initial layer of the compressible Euler equation, J. Math. Kyoto Univ. 26 (1986) 323-331. | MR 849223 | Zbl 0618.76074