Relative Entropy and the Stability of Shocks and Contact Discontinuities for Systems of Conservation Laws with non-BV Perturbations

By N. Leger, Alexis Vasseur. 2010

87 citations recorded by the source corpus.

We develop a theory based on relative entropy to show the uniqueness and L2 stability (up to a translation) of extremal entropic Rankine–Hugoniot discontinuities for systems of conservation laws (typically 1-shocks, n-shocks, 1-contact discontinuities and n-contact discontinuities of large amplitude) among bounded entropic weak solutions having an additional trace property. The existence of a convex entropy is needed. No BV estimate is needed on the weak solutions considered. The theory holds without smallness conditions. The assumptions are quite general. For instance, strict hyperbolicity is not needed globally. For fluid mechanics, the theory handles solutions with vacuums.

Subfields: Applied Mathematics, Computational Mechanics, Control and Systems Engineering

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In Applied Mathematics

In Computational Mechanics

In Control and Systems Engineering

Citations in the corpus

Criteria on Contractions for Entropic Discontinuities of Systems of Conservation Laws (2015, methodology): “The proof of this lemma can be found in [32, 53].”