Global smooth solutions of Euler equations for Van der Waals gases

2010/03/25 by Magali Mercier, Mercier, Magali
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP

paper · pdf · doi:10.48550/arxiv.1003.4903

arxiv created 2010/03/25 · arxiv updated 2010/04/07

Abstract

We prove global in time existence of solutions of the Euler compressible equations for a Van der Waals gas when the density is small enough in Hm, for m large enough. To do so, we introduce a specific symmetrisation allowing areas of null density. Next, we make estimates in Hm, using for some terms the estimates done by M. Grassin, who proved the same theorem in the easier case of a perfect polytropic gas. We treat the remaining terms separately, due to their non-linearity.

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