Comptes Rendus
no. 3
Partial differential equations
On the local existence for the Euler equations with free boundary for compressible and incompressible fluids

Presented by: the Editorial Board

Marcelo M. Disconzi1; Igor Kukavica2
1 Department of Mathematics, Vanderbilt University, Nashville, TN 37240, USA
2 Dept. of Mathematics, University of Southern California, Los Angeles, CA 90089-2532, USA
Comptes Rendus. Mathématique, Volume 356 (2018) no. 3, pp. 306-311.

We consider the free boundary compressible and incompressible Euler equations with surface tension. In both cases, we provide a priori estimates for the local existence with the initial velocity in H3, with the H3 condition on the density in the compressible case. An additional condition is required on the free boundary. Compared to the existing literature, both results lower the regularity of initial data for the Lagrangian Euler equation with surface tension.

Nous considérons les équations d'Euler compressibles et incompressibles avec frontière libre et tension de surface. Dans les deux cas, nous fournissons des estimations a priori pour l'existence de solutions locales avec vitesse initiale dans H3 et la condition H3 sur la densité dans le cas compressible. Une condition supplémentaire est nécessaire sur la frontière libre. Par comparaison avec la littérature, les deux résultats abaissent la régularité des données initiales pour les équations d'Euler en coordonnées lagrangiennes, avec tension de surface.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2018.02.002

Marcelo M. Disconzi 1; Igor Kukavica 2

1 Department of Mathematics, Vanderbilt University, Nashville, TN 37240, USA
2 Dept. of Mathematics, University of Southern California, Los Angeles, CA 90089-2532, USA 
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Marcelo M. Disconzi; Igor Kukavica. On the local existence for the Euler equations with free boundary for compressible and incompressible fluids. Comptes Rendus. Mathématique, Volume 356 (2018) no. 3, pp. 306-311. doi : 10.1016/j.crma.2018.02.002. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2018.02.002/

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