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Extended Divergence-Measure Fields and the Euler Equations for Gas Dynamics

#### Author: Gui-Qiang Chen and Hermano Frid

#### Title:
Extended Divergence-Measure Fields and the Euler Equations for Gas Dynamics

**Abstract**

A class of extended vector fields, called extended divergence-measure
fields, is analyzed. These fields include vector fields in $L^p$
and vector-valued Radon measures, whose divergences are Radon measures.
Such extended vector fields arise naturally in the study of
the behavior of entropy solutions to the Euler equations for gas
dynamics and other nonlinear systems of conservation laws.
A new notion of normal traces over Lipschitz deformable surfaces
is developed under which a generalized Gauss-Green theorem is
established even for these extended fields.
An explicit formula is obtained to calculate the normal traces
over any Lipschitz deformable surface, suitable for applications,
by using the neighborhood information of the fields near the surface
and the level set function of the Lipschitz deformation surfaces.
As an application, we prove the uniqueness and stability of Riemann
solutions that may contain vacuum in the class of entropy solutions
of the Euler equations for gas dynamics.

This article will appear in:

* Communications in Mathematical Physics
*, **Vol. 236**, pages 251-280 (2003)

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A closely related paper is Change me.

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