## Compressible Euler Equations with General Pressure Law

#### Authors: Gui-Qiang Chen and Philippe LeFloch

#### Title: Compressible Euler Equations with General Pressure Law

**Abstract**

We study the hyperbolic system of Euler equations for an isentropic,
compressible fluid governed by a general pressure law.
The existence and regularity of the {\it entropy kernel\/} that
generates the family of weak entropies is established by solving a new
Euler-Poisson-Darboux equation, which is {\it highly singular\/}
when the density of the fluid vanishes.
New properties of {\it cancellation of singularities\/} in combinations
of the entropy kernel and the associated entropy-flux kernel are found.
We prove the {\it strong compactness\/} of any
sequence that is uniformly bounded in $L^\infty$ and whose weak entropy
dissipation measures are locally $H^{-1}$ compact.
The {\it existence\/} and {\it large-time behavior\/} of $L^\infty$
entropy solutions of the Cauchy problem are established.
This is based on a reduction theorem for Young measures, whose
proof is new even for the polytropic perfect gas.
The existence result also extends to the {\it p-system\/} of fluid dynamics
in Lagrangian coordinates.

*Archive for Rational Mechanics and Analysis*, **vol 153**,
pages 221-259 (2000)

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A closely related paper is Change me.

**Author Address**
Gui-Qiang Chen
Department of Mathematics
Northwestern University
Evanston, IL 60208-2730
gqchen@math.nwu.edu