勷勤数学•专家报告

题      目：Zero-relaxation limits of the non-isentropic Euler-Maxwell system for well/ill-prepared initial data

报  告  人：冯跃红 副教授  (邀请人：李进开)

                                      北京工业大学数学统计学与力学学院

时      间： 12月28日  09：00-10:00

地     点：数科院西楼114

报告人简介:

           冯跃红，副教授。2003年本科毕业于河南大学；2008年硕士毕业于同一大学；2014年博士毕业于北京工业大学和法国克莱蒙大学；同年10月到北京工业大学工作，现为校研究生教学督导专家、应用数学研究所副所长。目前主要从事应用科学中的非线性偏微分方程定解问题解的适定性和渐近机制等领域的研究工作，在SIAM. J. Math. Anal.等期刊发表SCI论文30余篇；主持国家自然科学基金和北京市自然科学基金各一项。

摘      要：

        This talk is concerned with the zero-relaxation limits for periodic smooth solutions of the non-isentropic Euler-Maxwell system in a three dimensional torus prescribing the well/ill-prepared initial data. The non-isentropic Euler-Maxwell system can be reduced to a quasi-linear symmetric hyperbolic system of one order. By observing a special structure of the non-isentropic Euler-Maxwell system, we are able to decouple the system and develop a technique to achieve the a priori $H^s$ estimates, which guarantees the limit for the non-isentropic Euler-Maxwell system as the relaxation time $\tau \rightarrow 0$. We realize that the convergence rate of the temperature is the same as  the other unknowns in  the $ L^\infty (0, T_1; H^s)$, but the convergence rate of the temperature is slower than  the velocity in $ L^2 (0, T_1; H^s)$. The zero-relaxation limit presented here is the transport equation coupled with the drift-diffusion system. However, the limit of the isentropic Euler-Maxwell system is the classical drift-diffusion system. This shows the essential difference between the isentropic and non-isentropic Euler-Maxwell systems.  This talk is based on the collaboration work with Xin Li, Ming Mei and Shu Wang.

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