Quantum Systems: A Mathematical Journey from Few to Many Particles

Relative entropy applied to the study of stability of shocks for conservation laws, and application to asymptotic analysis

Alexis Vasseur

University of Texas at Austin

The relative entropy method is a powerful tool for the study of conservation laws. It provides, for example, the weak/strong uniqueness principle, and has been used in different context for the study of asymptotic limits. Up to now, the method was restricted to the comparison to Lipschitz solutions. This is because the method is based on the strong stability in L² of such solutions. Shocks are known to not be strongly L² stable. We show, however that their profiles are strongly L² stable up to a drift. We provide a first application of this stability result to the study of asymptotic limits.