Communications in Mathematical Sciences

Volume 4 (2006)

Number 3

Multiple solutions for compressible turbulent flow models

Pages: 497 – 511



Christophe Berthon

Frédéric Coquel


We analyse the uniqueness of the solutions of a PDE system from the framework of compressible turbulent models. Smoothness properties of the turbulent viscosity closure law are of central importance. Several closures of practical importance, including the most widely used law, indeed fail to be Lipschitz continuous in the natural neighborhood of a null turbulent energy. For such models, we prove the existence of infinitely many distinct traveling wave solutions which exhibit positive turbulent energy but connect at infinity end states with vanishing turbulence. Examples and counter-examples are given.


Traveling wave solutions; non-uniqueness; compressible gas dynamics systems

2010 Mathematics Subject Classification

Primary 35Q35. Secondary 35L67, 76Fxx, 76Nxx.

Published 1 January 2006