##
Uniqueness and Stability of Riemann Solutions with Large Oscillation
in Gas Dynamics

#### Authors: Gui-Qiang Chen, Hermano Frid, and Yachun Li

#### Title:
Uniqueness and Stability of Riemann Solutions with Large Oscillation
in Gas Dynamics

**Abstract**

We prove the uniqueness of Riemann solutions in the class of entropy
solutions in $L^\infty\cap BV_{loc}$ with arbitrarily large oscillation
for the $3\X3$ system of Euler equations in gas dynamics.
Our proof for solutions with {\it large} oscillation is based on
a detailed analysis of the global behavior of shock
curves in the phase space and the singularity of centered rarefaction
waves near the center in the physical plane.
The uniqueness of Riemann solutions yields their inviscid large-time
stability under {\it arbitrarily large} $L^1\cap L^\infty\cap BV_{loc}$
perturbation
of the Riemann initial data, as long as the corresponding solutions are
in $L^\infty$ and have local bounded total variation satisfying a natural
condition on its growth with time.
No specific reference to any particular method for constructing
the entropy solutions is made.
Our uniqueness result for Riemann solutions can be easily extended
to entropy solutions $U(x,t)$, piecewise Lipschitz in $x$,
for any $t>0$, with arbitrarily large oscillation.

This article has appeared in:

*Coomunications on Mathematical Physics (2001) *,
**vol#**, pages (2001)

This paper is available in the following formats:

A closely related paper is Change me.

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