Preprint 2004-001

Some Results on General System of Isentropic Gas Dynamics

Yunguang Lu

Abstract: In this paper, we construct a sequence of regular hyperbolic systems (\ref{1.1}) to approximate the general system of isentropic gas dynamics (\ref{1.2}). First, for each fixed approximation parameter $\delta$, we establish the existence of entropy solutions for the Cauchy problem (\ref{1.1}) with bounded initial date (\ref{1.4}). Second, letting $ \E=o(\delta)$, we obtain a simple proof of the $H_{loc}^{-1}$ compactness of weak entropy pairs of system (\ref{1.2}) in the form $ \eta( \rho,u)= \rho H(\rho,u)$ constructed in \cite{CL1,CL2}.

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Yunguang Lu, <>
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<> January 8 2004.

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