$L^2$ Stability and Weak-BV Uniqueness for Nonisentropic Euler Equations

Abstract

We prove the $L^2$ stability for weak solutions of non-isentropic Euler equations in one space dimension whose initial data are perturbed from a small BV data under the $L^2$ distance. Using this result, we can show the uniqueness of small BV solutions among a large family of weak solutions.