Analysis of incompressible plasmas at large values of the speed of light
数学专题报告
报告题目(Title)：Analysis of incompressible plasmas at large values of the speed of light
报告人(Speaker)：Dr. Haroune Houamed (纽约大学阿布扎比分校)
地点(Place)：Zoom 会议 ID：983 597 69042, 密码：123456, Zoom Link: https://zoom.us/j/98359769042
时间(Time)：2023 年 11 月 06 日（周一） 15:00--16:00
邀请人(Inviter)：薛留堂
报告摘要
The behavior of plasmas (electrically conducting fluids) is often well-described by a set of hydrodynamic equations coupled with Maxwell’s system 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 my 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 of 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 towards the end of the talk.
