题目：The L2 Theory for Compressible Euler Equations and the Vanishing Viscosity Limit

报告人：陈庚 副教授 （美国堪萨斯大学）

时间：2023年6月28日 （周三）15:00--16:00

地点：腾讯会议室

摘要：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, I will first discuss the recent result with Krupa and Vasseur for systems with two unknowns and non-isentropic Euler equations with three unknowns, where we established an L2 stability theory using the method of weighted relative entropy norm and modified front tracking scheme with shifts. As an application, we proved all BV solutions must satisfy the Bounded Variation Condition, which is a condition added by Bressan and etc to show uniqueness of solution. Hence, we showed the uniqueness of BV solution without any additional condition.

Then I will briefly introduce the recent progress on the vanishing viscosity limit from Navier-Stokes equations to the BV solution of compressible Euler equations. This is a famous open problem after Bressan-Bianchini’s seminal vanishing artificial viscosity limit result for BV solutions of hyperbolic conservation laws. This is a join work with Kang and Vasseur.

腾讯会议：465272038 会议密码：444499

报告人简介：陈庚，美国University of Kansas副教授，2010年博士毕业于美国University of Massachusetts Amherst，主要研究方向为非线性偏微分方程、流体力学和数学物理，在可压缩欧拉方程组、非线性波方程和浅水波方程等模型解的适定性研究上取得了一系列重要成果，在Arch. Ration. Mech. Anal.、 J. Math. Pures Appl.、Ann. Inst. H. Poincaré Anal. Non Linéaire、Comm. PDE、SIAM J. Math. Anal.、Indiana Univ. Math. J.等国际著名学术期刊发表论文数十篇。

欢迎各位参加！