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September 2006 Multiple solutions for compressible turbulent flow models
Christophe Berthon, Frédéric Coquel
Commun. Math. Sci. 4(3): 497-511 (September 2006).


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.


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Christophe Berthon. Frédéric Coquel. "Multiple solutions for compressible turbulent flow models." Commun. Math. Sci. 4 (3) 497 - 511, September 2006.


Published: September 2006
First available in Project Euclid: 5 April 2007

zbMATH: 1109.35073
MathSciNet: MR2247928

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

Keywords: compressible gas dynamics systems , non-uniqueness , traveling wave solutions

Rights: Copyright © 2006 International Press of Boston

Vol.4 • No. 3 • September 2006
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