Asymptotic limit to a shock for BGK models using relative entropy method

Abstract

We consider the hydrodynamic limit of a kinetic BGK model in one space dimension, to a scalar conservation law with a strict convex flux. In this paper, we provide sharp estimates for the asymptotic limit to shocks, where layers, called Knudsen layers, may appear. The used method is based on the relative entropy. It follows a previous work of Choi and Vasseur (arXiv:1210.7853 preprint) where similar sharp estimates were obtained for the inviscid limit of a viscous conservation laws to a shock.