**Nicholas Leger**

**Afilliation:**Carnegie Mellon University

**Title:**Relative entropy and the stability of shocks and contact discontinuities for systems of conservation laws

**Abstract:**We develop a theory based on relative entropy to show the stability and uniqueness 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 a suitable 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 condition. The assumptions are quite general. For instance, strict hyperbolicity is not needed globally. For fluid mechanics, the theory handles solutions with vacuum.

**Slides:**LegerNicholas.pdf