The stability of shock waves and the physical inviscid limit
报告题目(Title)：The stability of shock waves and the physical inviscid limit
报告人(Speaker)：陈庚 教授（美国堪萨斯大学）
地点(Place)：后主楼1124
时间(Time)：2026年6月26日（周五）15:00-16:00
邀请人(Inviter)：李林安
报告摘要
In this talk, several recent advances on the shock wave theory will be discussed.
The solutions of compressible Euler equations often form shock waves, in finite time, notably observed behind supersonic planes. A very natural way to justify these singularities involves studying solutions from inviscid limits of Navier-Stokes solutions. The mathematical study of this problem is however very difficult because of the destabilization effect of the viscosities. Bianchini and Bressan proved the inviscid limit to small BV solutions in one space dimension using the so-called artificial viscosities in 2004. However, until recently, achieving this limit with physical viscosities remained an open question. In this presentation, the recent advances (join with Krupa and Vasseur) on the L2 theory of compressible fluid mechanics will be introduced. This method is employed to describe the physical inviscid limit in the context of the barotropic Euler equations, and to solve the Bianchini and Bressan's conjecture. This is a joint work with Kang and Vasseur.
Then I will introduce the very recent progress with Fail and Krupa on the Holder stability for Euler equations.
主讲人简介
陈庚教授现任美国堪萨斯大学数学系G. Bailey Price讲席教授，并担任研究生招生主任。他于2010年在美国麻省大学阿默斯特分校获得数学博士学位，先后在宾州州立大学和佐治亚理工学院从事博士后研究工作。陈庚教授的主要研究方向为非线性偏微分方程、流体力学和数学物理。目前的研究聚焦于双曲守恒律、可压缩Euler方程和Navier-Stokes方程，以及非线性波现象。他在可压缩Euler方程组解的奇异性、唯一性及L2稳定性方面取得一系列系统性重要成果。其研究成果发表在Arch. Ration. Mech. Anal.、Comm. Math. Phys.、J. Math. Pures Appl.、J. Lond. Math. Soc.、Ann. Inst. H. Poincaré Anal. Non Linéaire、Comm. PDE、SIAM J. Math. Anal.、Indiana Univ. Math. J.等国际权威学术期刊上。
