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Entropy criteria and stability of extreme shocks: a remark on a paper of Leger and Vasseur
- Source :
- Proceedings of the American Mathematical Society. 143:749-754
- Publication Year :
- 2014
- Publisher :
- American Mathematical Society (AMS), 2014.
-
Abstract
- We show that a relative entropy condition recently shown by Leger and Vasseur to imply uniqueness and stable $L^2$ dependence on initial data of Lax 1- or $n$-shock solutions of an $n\times n$ system of hyperbolic conservation laws with convex entropy implies Lopatinski stability in the sense of Majda. This means in particular that Leger and Vasseur's relative entropy condition represents a considerable improvement over the standard entropy condition of decreasing shock strength and increasing entropy along forward Hugoniot curves, which, in a recent example exhibited by Barker, Freist\"uhler and Zumbrun, was shown to fail to imply Lopatinski stability, even for systems with convex entropy. This observation bears also on the parallel question of existence, at least for small $BV$ or $H^s$ perturbations<br />Comment: to appear in Proceedings of the AMS
- Subjects :
- Conservation law
Kullback–Leibler divergence
Standard molar entropy
Applied Mathematics
General Mathematics
010102 general mathematics
Mathematical analysis
Mathematics::Analysis of PDEs
Regular polygon
Min entropy
Shock strength
01 natural sciences
010101 applied mathematics
Mathematics - Analysis of PDEs
FOS: Mathematics
Uniqueness
0101 mathematics
Analysis of PDEs (math.AP)
Mathematics
Subjects
Details
- ISSN :
- 10886826 and 00029939
- Volume :
- 143
- Database :
- OpenAIRE
- Journal :
- Proceedings of the American Mathematical Society
- Accession number :
- edsair.doi.dedup.....0ff114b103abe7f546c786ddb4c64527