Uniqueness of BV solution for compressible Euler equations

时   间：  2022-08-28 10:30 — 11:30

Compressible Euler equations are a typical system of hyperbolic conservation laws, whose solution forms shock waves in general. It is well known that global BV solutions of system of hyperbolic conservation laws exist, when one considers small BV initial data. In this talk, we will present our recent proof on uniqueness of BV solution.

As a major breakthrough for system of hyperbolic conservation laws in 1990’s, by Bressan and his collaborators, solutions have been proved to be unique among BV solutions verifying either the so-called Tame Oscillation Condition, or the Bounded Variation Condition on space-like curves.

In this talk, we show that these solutions are stable in a larger class of weak (and possibly not even BV) solutions of the system. As a consequence of our result, one does not have to assume the Bounded Variation Condition on space-like curves in the uniqueness theory, for systems with two unknowns and non-isentropic Euler equations. Hence, the uniqueness of BV solution is proved. This is a joint work with Sam Krupa and Alexis Vasseur.

报告人简介： 

       陈庚，美国堪萨斯大学副教授。博士毕业于麻省大学，曾先后在宾州州立大学及佐治亚理工学院做博士后。在双曲型方程组解的奇异性及唯一性等领域取得系统性的重要研究成果，发表在ARMA, JMPA, CPDE等国际权威期刊上。