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arXiv · 1003.4903

Global smooth solutions of Euler equations for Van der Waals gases

Magali Mercier
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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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Magali Mercier. 2010-03-25. Global smooth solutions of Euler equations for Van der Waals gases. https://arxiv.org/abs/1003.4903

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