37000gcom威尼斯2023年第31期数理大讲堂

报告题目：Global-in-time Unique Solutions of the Incompressible Euler–Maxwell System in Two-Dimensions

报告人：Dr.Haroune Houamed

报告时间：2023年10月25日（19：00-20：30）

报告地点：腾讯会议线上(会议号：136314675）

邀请人：周勇教授

摘要：

The behavior of plasmas (electrically conducting fluids) is often well-described by a set of hydrodynamic equations coupled with Maxwell’s equations through the action of an electromagnetic force. Many aspects of the analysis of such models are met with important challenges due to the hyperbolic nature of Maxwell’s system.

In this talk, I will focus on the two-dimensional Euler--Maxwell equations, which describe the evolution of ideal plasmas. After introducing the settings of the equations, I will explain how to extend Yudovich’s method to construct a unique global-in-time solution to these equations. It is also to be emphasized that our method of proof allows us to obtain bounds on the solution which are uniform with respect to the speed of light c \in (c_0,\infty), for some threshold parameter c_0>0 which only depends on the size of the given initial data. Therefore, as a by-product of an additional refined analysis of Ampere's equation, we are capable of giving a precise description of the limit c \to \infty in strong topologies, thereby deriving (simple 2D version of) the MHD system. Other more recent and ongoing works will also be briefly discussed at the end.

专家简介：纽约大学博士后