Archive for Rational Mechanics and Analysis

, Volume 219, Issue 2, pp 679–699 | Cite as

Long-time Stability in Systems of Conservation Laws, Using Relative Entropy/Energy

  • Denis SerreEmail author


We study the long-time stability of shock-free solutions of hyperbolic systems of conservation laws, under an arbitrarily large initial disturbance in L 2L . We use the relative entropy method, a robust tool which allows us to consider rough and large disturbances. We display practical examples in several space dimensions, for scalar equations as well as isentropic gas dynamics. For full gas dynamics, we use a trick from Chen [1], in which the estimate is made in terms of the relative mechanical energy instead of the relative mathematical entropy.


Entropy Relative Entropy Rarefaction Wave Entropy Solution Euler System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.UMPA, UMR CNRS–ENS Lyon # 5669, École Normale Supérieure de LyonLyon Cedex 07France

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