报告人：寿凌云

报告时间：2025年1月4日上午9:00

报告地点：东校区办公楼704

Abstract:

Westudy the relaxed compressible Euler-Maxwell system, a classical modeldescribing plasma dynamics. First, we prove the global existence of classicalsolutions to the Cauchy problem for small perturbations of the constantequilibrium within a critical regularity framework and establish qualitativeregularity estimates with respect to the relaxation parameter. Next, we deriveglobal error estimates with a sharp convergence rate between the scaledEuler-Maxwell system and the limiting drift-diffusion model in the case ofill-prepared data.

Comparedwith dissipative hyperbolic systems with symmetric relaxation, the mainchallenge lies in that the Euler-Maxwell system has a regularity-lossphenomenon caused by the non symmetric structure. To overcome this difficulty,we develop a new characterization of the dissipation structure for theEuler-Maxwell system with respect to the relaxation parameter. This involvespartitioning the frequency space into three distinct regimes: low, medium, andhigh frequencies, associated with different behaviors of the solution. Indifferent frequency regimes, the Lyapunov functionals based on thehypocoercivity theory are used to establish uniform a priori estimates. Moreover, the global-in-time convergence rate is obtained by using an effectiveunknown associated with Darcy’s law.  This work is a collaboration withTimothée Crin-Barat, Yue-Jun Peng and Jiang Xu.

报告人简介：寿凌云，博士，南京师范大学，研究方向为偏微分方程理论及其应用。主持国家自然科学青年基金1项，中国博士后基金1项。在Adv.Math., Sci. China Math., SIAM J.Math.Anal., J. Differential Equations,Nonlinearity等国际著名期刊发表论文数篇。