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Existence of global weak solution for compressible fluid models with a capillary tensor for discontinuous interfaces

Haspot, Boris (2010), Existence of global weak solution for compressible fluid models with a capillary tensor for discontinuous interfaces, Differential and Integral Equations, 23, 9-10, p. 899-934

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http://hal.archives-ouvertes.fr/hal-00776872
Date
2010
Nom de la revue
Differential and Integral Equations
Volume
23
Numéro
9-10
Éditeur
Khayyam Publishing Company
Pages
899-934
Métadonnées
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Auteur(s)
Haspot, Boris
Résumé (EN)
This work is devoted to proving the global existence of weak solution for a general isothermal model of capillary fluids derived in his modern form by C. Rohde in [21], which can be used as a phase transition model. First, inspired by the result by P.-L. Lions in [19] on the Navier- Stokes compressible system we show the global stability of weak solutions for our system with is entropic pressure and next with general pressure. Finally, we consider perturbations of a stable equilibrium.
Mots-clés
Navier–Stokes system; capillary fluids