@article{SEDP_2000-2001____A3_0, author = {Danchin, Rapha\"el}, title = {Fluides l\'eg\`erement compressibles et limite incompressible}, journal = {S\'eminaire \'Equations aux d\'eriv\'ees partielles (Polytechnique) dit aussi "S\'eminaire Goulaouic-Schwartz"}, note = {talk:3}, publisher = {Centre de math\'ematiques Laurent Schwartz, \'Ecole polytechnique}, year = {2000-2001}, mrnumber = {1860675}, zbl = {1061.35511}, language = {fr}, url = {http://www.numdam.org/item/SEDP_2000-2001____A3_0/} }
TY - JOUR AU - Danchin, Raphaël TI - Fluides légèrement compressibles et limite incompressible JO - Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" N1 - talk:3 PY - 2000-2001 DA - 2000-2001/// PB - Centre de mathématiques Laurent Schwartz, École polytechnique UR - http://www.numdam.org/item/SEDP_2000-2001____A3_0/ UR - https://www.ams.org/mathscinet-getitem?mr=1860675 UR - https://zbmath.org/?q=an%3A1061.35511 LA - fr ID - SEDP_2000-2001____A3_0 ER -
Danchin, Raphaël. Fluides légèrement compressibles et limite incompressible. Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" (2000-2001), Exposé no. 3, 17 p. http://www.numdam.org/item/SEDP_2000-2001____A3_0/
[AT] P. Auscher et P. Tchamitchian : Espaces critiques pour le système des équations de Navier-Stokes incompressibles, Prépublication de l’Université de Picardie Jules Verne (1999).
[BKM] J. Beale, T. Kato et A. Majda : Remarks on the breakdown of smooth solutions for the 3-D Euler equations, Communications in Mathematical Physics, 94, pages 61–66 (1984). | MR 763762 | Zbl 0573.76029
[Bon] J.-M. Bony : Calcul symbolique et propagation des singularités pour les équations aux dérivées partielles non linéaires, Annales Scientifiques de l’École Normale Supérieure, 14, pages 209–246 (1981). | Numdam | Zbl 0495.35024
[Bou] G. Bourdaud : Réalisations des espaces de Besov homogènes, Arkiv för matematik, 26, pages 41–54 (1988). | MR 948279 | Zbl 0661.46026
[Da1] R. Danchin : Global existence in critical spaces for compressible Navier-Stokes equations, Inventiones Mathematicae, 141, pages 579–614 (2000) | MR 1779621 | Zbl 0958.35100
[Da2] R. Danchin : Local theory in critical spaces for compressible viscous and heat-conductive gases, to appear in Communications in Partial Differential Equation. | MR 1855277 | Zbl 1007.35071
[Da3] R. Danchin : Zero Mach number limit in critical spaces for compressible Navier-Stokes equations, to appear in Annales Scientifiques de l’École Normale Supérieure. | Numdam | Zbl 1048.35054
[Da4] R. Danchin : Zero Mach number limit for compressible Navier-Stokes equations with periodic boundary conditions, travail en cours. | Zbl 1048.35075
[DG] B. Desjardins and E. Grenier : Low Mach number limit of viscous compressible flows in the whole space, Royal Society of London Proceedings, Series A, 455 (1986), pages 2271–2279 (1999). | MR 1702718 | Zbl 0934.76080
[DGLM] B. Desjardins, E. Grenier, P.-L. Lions and N. Masmoudi : Incompressible limit for solutions of the isentropic Navier-Stokes equations with Dirichlet boundary conditions, Journal de Mathématiques Pures et Appliquées, 78, pages 461–471 (1999). | MR 1697038 | Zbl 0992.35067
[FK] H. Fujita and T. Kato : On the Navier-Stokes initial value problem I, Archive for Rational Mechanics and Analysis, 16, pages 269–315 (1964). | MR 166499 | Zbl 0126.42301
[G] I. Gallagher : A remark on smooth solutions of the weakly compressible periodic Navier-Stokes equations, prépublication Université Paris-Sud, Mathématiques (1999). | MR 1794519 | Zbl 0997.35050
[GV] J. Ginibre and G. Velo : Generalized Strichartz inequalities for the wave equation, Journal of Functional Analysis, 133, pages 50–68 (1995). | MR 1351643 | Zbl 0849.35064
[HL] T. Hagstrom and J. Lorenz : All-time existence of classical solutions for slightly compressible flows, SIAM Journal on Mathematical Analysis, 29, pages 652–672 (1998). | MR 1617767 | Zbl 0907.76073
[Ho] D. Hoff : The zero-Mach limit of compressible flows, Communications in Mathematical Physics, 192, pages 543–554 (1998). | MR 1620511 | Zbl 0907.35098
[KM] S. Klainerman and A. Majda : Compressible and incompressible fluids, Communications in Pure and Applied Mathematics, 35, pages 629–651 (1982). | MR 668409 | Zbl 0478.76091
[KLN] H.-0. Kreiss, J. Lorenz and M. Naughton : Convergence of the solutions of the compressible to the solutions of the incompressible Navier-Stokes equations, Advances in Pure and Applied Mathematics, 12, pages 187–214 (1991). | MR 1101207 | Zbl 0728.76084
[Le] J. Leray : Sur le mouvement d’un liquide visqueux remplissant l’espace, Acta mathematica, 63, pages 193–248 (1934).
[Li1] P.-L. Lions : Mathematical topics in fluid mechanics, vol. 1, incompressible models (1996). | MR 1422251 | Zbl 0866.76002
[Li2] P.-L. Lions : Mathematical topics in fluid mechanics, vol. 2, compressible models (1998). | MR 1637634 | Zbl 0908.76004
[LM1] P.-L. Lions, N. Masmoudi : Incompressible limit for a viscous compressible fluid, Journal de Mathématiques Pures et Appliquées, 77, pages 585–627 (1998). | MR 1628173 | Zbl 0909.35101
[LM2] P.-L. Lions, N. Masmoudi : Une approche locale de la limite incompressible, Comptes-Rendus de l’Académie des Sciences, Paris, Série I, 329, pages 387–392 (1999). | Zbl 0937.35132
[M] Y. Meyer : Wavelets, paraproducts, and Navier-Stokes equations. Current developments in mathematics, (Cambridge, MA), Int. Press, Boston, pages 105–212 (1996). | MR 1724946 | Zbl 0926.35115
[RS] T. Runst and W. Sickel : Sobolev spaces of fractional order, Nemytskij operators, and nonlinear partial differential equations. de Gruyter Series in Nonlinear Analysis and Applications, 3. Walter de Gruyter & Co., Berlin (1996). | MR 1419319 | Zbl 0873.35001
[St] R. Strichartz : Restriction of Fourier transform to quadratic surfaces and decay of solutions of wave equations, Duke Mathematical Journal, 44, pages 705–774 (1977). | MR 512086 | Zbl 0372.35001