勷勤数学•专家报告

题      目：The Euler-Maxwell system: Frequency splitting,  hypocoercivity and relaxation limit

报  告  人：寿凌云  讲师  (邀请人：罗天文)

                                 南京师范大学

时      间：11月14日  09：30-10：30

地     点：数科院西楼114教室

报告人简介:

       寿凌云，目前任职于南京师范大学，主要从事偏微分方程的研究，研究方向为Fourier分析及其应用，在关于流体力学方程的长时间行为、双曲松弛系统奇异极限方面做了一些工作。

摘      要：

       We study the damped compressible Euler-Maxwell system, a classical model describing the interaction of electrons with electromagnetic waves in semiconductor devices. First, we prove the global existence of classical solutions to the Cauchy problem for small perturbations of the constant equilibrium within a critical regularity framework, uniformly with respect to the relaxation parameter. Next, we derive global error estimates with a sharp convergence rate between the scaled Euler-Maxwell system and the limiting drift-diffusion model in the case of ill-prepared data.
  To achieve our results, we develop a new characterization of the dissipation structure for the Euler-Maxwell system with respect to the relaxation parameter. This involves partitioning the frequency space into three distinct regimes: low, medium, and high frequencies, associated with different behaviors of the solution. In different frequency regimes, the Lyapunov functionals based on the hypocoercivity theory are used to establish uniform a priori estimates.  In addition, the global-in-time convergence rate is obtained by using an effective unknown associated with Darcy’s law. This work is a collaboration with Dr. Timothée Crin-Barat, Prof. Yue-Jun Peng and Prof. Jiang Xu.

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