[Limite incompressible de solutions du système d'Euler compressible correspondant à des données initiales dont la régularité dégénère]
En utilisant des inégalités de Strichartz, il est possible de passer à la limite dans le système d'Euler compressible 2-D, quand le nombre de Mach tend vers zéro, même si les données initiales ne sont pas uniformément régulières. Ceci mène à des résultats de convergence vers des solutions du système d'Euler incompressible dont la régularité est critique, comme des poches de tourbillon ou des solutions de Yudovich.
Using Strichartz estimates, it is possible to pass to the limit in the weakly compressible 2-D Euler system, when the Mach number ε tends to zero, even if the initial data are not uniformly smooth. This leads to results of convergence to solutions of the incompressible Euler system whose regularity is critical, such as vortex patches or Yudovich solutions.
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@article{CRMATH_2003__336_6_471_0,
author = {Dutrifoy, Alexandre and Hmidi, Taoufik},
title = {The incompressible limit of solutions of the two-dimensional compressible {Euler} system with degenerating initial data},
journal = {Comptes Rendus. Math\'ematique},
pages = {471--474},
publisher = {Elsevier},
volume = {336},
number = {6},
year = {2003},
doi = {10.1016/S1631-073X(03)00100-6},
language = {en},
url = {http://www.numdam.org/articles/10.1016/S1631-073X(03)00100-6/}
}
TY - JOUR AU - Dutrifoy, Alexandre AU - Hmidi, Taoufik TI - The incompressible limit of solutions of the two-dimensional compressible Euler system with degenerating initial data JO - Comptes Rendus. Mathématique PY - 2003 SP - 471 EP - 474 VL - 336 IS - 6 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/S1631-073X(03)00100-6/ DO - 10.1016/S1631-073X(03)00100-6 LA - en ID - CRMATH_2003__336_6_471_0 ER -
%0 Journal Article %A Dutrifoy, Alexandre %A Hmidi, Taoufik %T The incompressible limit of solutions of the two-dimensional compressible Euler system with degenerating initial data %J Comptes Rendus. Mathématique %D 2003 %P 471-474 %V 336 %N 6 %I Elsevier %U http://www.numdam.org/articles/10.1016/S1631-073X(03)00100-6/ %R 10.1016/S1631-073X(03)00100-6 %G en %F CRMATH_2003__336_6_471_0
Dutrifoy, Alexandre; Hmidi, Taoufik. The incompressible limit of solutions of the two-dimensional compressible Euler system with degenerating initial data. Comptes Rendus. Mathématique, Tome 336 (2003) no. 6, pp. 471-474. doi : 10.1016/S1631-073X(03)00100-6. http://www.numdam.org/articles/10.1016/S1631-073X(03)00100-6/
[1] Perfect Incompressible Fluids, Oxford Lecture Series in Math. Appl., 14, The Clarendon Press–Oxford University Press, New York, 1998 (Translated from the 1995 French original by Isabelle Gallagher and Dragos Iftimie)
[2] Low Mach number limit of viscous compressible flows in the whole space, Roy. Soc. London Proc. Ser. A Math. Phys. Eng. Sci., Volume 455 (1999) no. 1986, pp. 2271-2279
[3] A. Dutrifoy, T. Hmidi, The incompressible limit of solutions of the two-dimensional compressible Euler system with degenerating initial data
[4] On three-dimensional vortex patches, Bull. Soc. Math. France, Volume 123 (1995) no. 3, pp. 375-424
[5] Generalized Strichartz inequalities for the wave equation, J. Funct. Anal., Volume 133 (1995) no. 1, pp. 50-68
[6] Singular limits of quasilinear hyperbolic systems with large parameters anf the incompressible limit of compressible fluids, Comm. Pure Appl. Math., Volume 34 (1981) no. 4, pp. 481-524
[7] The incompressible limit and the initial layer of the compressible Euler equation, J. Math. Kyoto Univ., Volume 26 (1986) no. 2, pp. 323-331
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