Comptes Rendus
Partial Differential Equations/Mathematical Problems in Mechanics
The incompressible limit of solutions of the two-dimensional compressible Euler system with degenerating initial data
[Limite incompressible de solutions du système d'Euler compressible correspondant à des données initiales dont la régularité dégénère]
Comptes Rendus. Mathématique, Volume 336 (2003) no. 6, pp. 471-474.

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.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/S1631-073X(03)00100-6

Alexandre Dutrifoy 1 ; Taoufik Hmidi 2

1 Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie, boı̂te courrier 187, 75252 Paris cedex 05, France
2 Centre de mathématiques, École polytechnique, 91128 Palaiseau cedex, France
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Alexandre Dutrifoy; Taoufik Hmidi. The incompressible limit of solutions of the two-dimensional compressible Euler system with degenerating initial data. Comptes Rendus. Mathématique, Volume 336 (2003) no. 6, pp. 471-474. doi : 10.1016/S1631-073X(03)00100-6. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(03)00100-6/

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[3] A. Dutrifoy, T. Hmidi, The incompressible limit of solutions of the two-dimensional compressible Euler system with degenerating initial data

[4] P. Gamblin; X. Saint Raymond On three-dimensional vortex patches, Bull. Soc. Math. France, Volume 123 (1995) no. 3, pp. 375-424

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