Fluides légèrement compressibles et limite incompressible
- [1] Laboratoire d’Analyse Numérique, 175 rue Chevaleret, Université Pierre et Marie Curie, 75252 Paris, France
Séminaire Équations aux dérivées partielles (2000-2001)
- Volume: 2000-2001, page 1-17
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topDanchin, Raphaël. "Fluides légèrement compressibles et limite incompressible." Séminaire Équations aux dérivées partielles 2000-2001 (2000-2001): 1-17. <http://eudml.org/doc/11022>.
@article{Danchin2000-2001,
affiliation = {Laboratoire d’Analyse Numérique, 175 rue Chevaleret, Université Pierre et Marie Curie, 75252 Paris, France},
author = {Danchin, Raphaël},
journal = {Séminaire Équations aux dérivées partielles},
keywords = {weakly compressible fluid; Besov space; paraproduct; Littlewood-Paley decomposition; zero-Mach limit},
language = {fre},
pages = {1-17},
publisher = {Centre de mathématiques Laurent Schwartz, École polytechnique},
title = {Fluides légèrement compressibles et limite incompressible},
url = {http://eudml.org/doc/11022},
volume = {2000-2001},
year = {2000-2001},
}
TY - JOUR
AU - Danchin, Raphaël
TI - Fluides légèrement compressibles et limite incompressible
JO - Séminaire Équations aux dérivées partielles
PY - 2000-2001
PB - Centre de mathématiques Laurent Schwartz, École polytechnique
VL - 2000-2001
SP - 1
EP - 17
LA - fre
KW - weakly compressible fluid; Besov space; paraproduct; Littlewood-Paley decomposition; zero-Mach limit
UR - http://eudml.org/doc/11022
ER -
References
top- 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).
- 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). Zbl0573.76029MR763762
- 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). Zbl0495.35024
- G. Bourdaud : Réalisations des espaces de Besov homogènes, Arkiv för matematik, 26, pages 41–54 (1988). Zbl0661.46026MR948279
- R. Danchin : Global existence in critical spaces for compressible Navier-Stokes equations, Inventiones Mathematicae, 141, pages 579–614 (2000) Zbl0958.35100MR1779621
- R. Danchin : Local theory in critical spaces for compressible viscous and heat-conductive gases, to appear in Communications in Partial Differential Equation. Zbl1007.35071MR1855277
- R. Danchin : Zero Mach number limit in critical spaces for compressible Navier-Stokes equations, to appear in Annales Scientifiques de l’École Normale Supérieure. Zbl1048.35054
- R. Danchin : Zero Mach number limit for compressible Navier-Stokes equations with periodic boundary conditions, travail en cours. Zbl1048.35075
- 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). Zbl0934.76080MR1702718
- 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). Zbl0992.35067MR1697038
- H. Fujita and T. Kato : On the Navier-Stokes initial value problem I, Archive for Rational Mechanics and Analysis, 16, pages 269–315 (1964). Zbl0126.42301MR166499
- I. Gallagher : A remark on smooth solutions of the weakly compressible periodic Navier-Stokes equations, prépublication Université Paris-Sud, Mathématiques (1999). Zbl0997.35050MR1794519
- J. Ginibre and G. Velo : Generalized Strichartz inequalities for the wave equation, Journal of Functional Analysis, 133, pages 50–68 (1995). Zbl0849.35064MR1351643
- 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). Zbl0907.76073MR1617767
- D. Hoff : The zero-Mach limit of compressible flows, Communications in Mathematical Physics, 192, pages 543–554 (1998). Zbl0907.35098MR1620511
- S. Klainerman and A. Majda : Compressible and incompressible fluids, Communications in Pure and Applied Mathematics, 35, pages 629–651 (1982). Zbl0478.76091MR668409
- 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). Zbl0728.76084MR1101207
- J. Leray : Sur le mouvement d’un liquide visqueux remplissant l’espace, Acta mathematica, 63, pages 193–248 (1934).
- P.-L. Lions : Mathematical topics in fluid mechanics, vol. 1, incompressible models (1996). Zbl0866.76002MR1422251
- P.-L. Lions : Mathematical topics in fluid mechanics, vol. 2, compressible models (1998). Zbl0908.76004MR1637634
- P.-L. Lions, N. Masmoudi : Incompressible limit for a viscous compressible fluid, Journal de Mathématiques Pures et Appliquées, 77, pages 585–627 (1998). Zbl0909.35101MR1628173
- 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). Zbl0937.35132
- Y. Meyer : Wavelets, paraproducts, and Navier-Stokes equations. Current developments in mathematics, (Cambridge, MA), Int. Press, Boston, pages 105–212 (1996). Zbl0926.35115MR1724946
- 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). Zbl0873.35001MR1419319
- R. Strichartz : Restriction of Fourier transform to quadratic surfaces and decay of solutions of wave equations, Duke Mathematical Journal, 44, pages 705–774 (1977). Zbl0372.35001MR512086
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