Criteria on Contractions for Entropic Discontinuities of Systems of Conservation Laws

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We study the contraction properties (up to shift) for admissible Rankine-Hugoniot discontinuities of systems of conservation laws endowed with a convex entropy. We first generalize the criterion developed in (Serre and Vasseur, J l'Ecole Polytech 1, 2014), using the spatially inhomogeneous pseudo-distance introduced in (Vasseur, Contemp Math AMS, 2013). Our generalized criterion guarantees the contraction property for extremal shocks of a large class of systems, including the Euler system. Moreover, we introduce necessary conditions for contraction, specifically targeted for intermediate shocks. As an application, we show that intermediate shocks of the two-dimensional isentropic magnetohydrodynamics do not verify any of our contraction properties. We also investigate the contraction properties, for contact discontinuities of the Euler system, for a certain range of contraction weights. None of the results involve any smallness condition on the initial perturbation or on the size of the shock.
Publisher
SPRINGER
Issue Date
2016-10
Language
English
Article Type
Article
Citation

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, v.222, no.1, pp.343 - 391

ISSN
0003-9527
DOI
10.1007/s00205-016-1003-1
URI
http://hdl.handle.net/10203/278727
Appears in Collection
MA-Journal Papers(저널논문)
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