报告题目：The two-dimensional plasma-vacuum interface problem in ideal MHD

报告时间：2024-04-17   16:50-17:30

报 告 人：Assoc. Prof. Alessandro Morando(University of  Brescia)

报告地点：理学院东北楼四楼报告厅（404）

Abstract：In this talk we consider the two-dimensional plasma-vacuum interface problem in ideal compressible magnetohydrodynamics (MHD). This is a hyperbolic-elliptic coupled system with a characteristic free boundary. In the plasma region the 2D planar flow is governed by the hyperbolic equations of ideal compressible MHD, while in the vacuum region the magnetic field obeys the elliptic system of pre-Maxwell dynamics. At the free interface moving with the velocity of plasma particles, the total pressure is continuous and the magnetic field on both sides is tangent to the boundary. The plasma-vacuum system is not isolated from the outside world, since it is driven by a given surface current which forces oscillations onto the system. We present our result about the local-in-time existence and uniqueness of solutions to the nonlinear free boundary problem, provided that the plasma magnetic field or the vacuum magnetic field is non-zero at each point of the initial interface. The proof follows from the analysis of the linearized MHD equations in the plasma region and the elliptic system for the vacuum magnetic field, suitable tame estimates in Sobolev spaces for the full linearized problem, and a Nash-Moser iteration. This is a joint work with P. Secchi (Brescia), Y. Trakhinin(Novosibirsk), P. Trebeschi(Brescia) and D. Yuan (Beijing Normal Univ.).