勷勤数学•专家报告

题      目：Weak stability of nonuniformly stable multidimensional shocks

报  告  人：张澜 副教授  (邀请人：袁源)

                                             武汉理工大学

时      间： 9月5日  16：30-17:30

地     点：数科院西楼114教室

报告人简介:

         张澜博士毕业于武汉大学，现于武汉理工大学数学与统计学院工作，曾在意大利布雷西亚大学从事博士后研究。主要研究方向为流体力学中的偏微分方程，主要工作发表在SIAM-JMA, Science China Math, JDE等国际数学期刊。

摘      要：

        We consider the weak stability of shock waves for the multidimensional Euler equations. In the monograph of Majda, he established the uniform stability condition for multidimensional shocks and proved the existence and stability of solutions. Specifically, for pressure obeying the gamma-law, shock profiles are necessarily uniformly stable. For pressure laws that are only monotonically increasing, shock profiles exhibit weak stability. Coulombel established the weak stability and existence of shock waves, yet left the critical case unresolved. We will address this open problem.

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