# Expansion of a compressible gas in vacuum

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1 UMPA-ENSL - Unité de Mathématiques Pures et Appliquées

Abstract : Tai-Ping Liu \cite{Liu JJ} introduced the notion of -physical solution- of the isentropic Euler system when the gas is surrounded by vacuum. This notion can be interpreted by saying that the front is driven by a force resulting from a H\-older singularity of the sound speed. We address the question of when this acceleration appears or when the front just move at constant velocity.We know from \cite{Gra,SerAIF} that smooth isentropic flows with a non-accelerated front exist globally in time, for suitable initial data. In even space dimension, these solutions may persist for all $t\in\R$ ; we say that they are {\em eternal}. We derive a sufficient condition in terms of the initial data, under which the boundary singularity must appear. As a consequence, we show that, in contrast to the even-dimensional case, eternal flows with a non-accelerated front don-t exist in odd space dimension.In one space dimension, we give a refined definition of physical solutions. We show that for a shock-free flow, their asymptotics as both ends $t ightarrow\pm\infty$ are intimately related to each other.

Autor: Denis Serre -

Fuente: https://hal.archives-ouvertes.fr/

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