报告题目：Nonlinear stability of two-dimensional compressible current-vortex sheets

报告时间：2024-04-17  16:00-16:40

报 告 人：Assoc. Prof. Paola Trebeschi(University of  Brescia)

报告地点：理学院东北楼四楼报告厅（404）

Abstract：In this talk we are concerned with nonlinear stability and existence of two-dimensional current-vortex sheets in ideal compressible magnetohydrodynamics. This is a nonlinear hyperbolic initial-boundary value problem with characteristic free boundary. It is well-known that current-vortex sheets may be at most weakly (neutrally) stable due to the existence of surface waves solutions that yield a loss of derivatives in the energy estimate of the solution with respect to the source terms. We first identify a sufficient condition ensuring the weak stability of the linearized current-vortex sheets problem. Under this stability condition for the background state, we show that the linearized problem obeys an energy estimate in anisotropic weighted Sobolev spaces with a loss of derivatives. Based on the weakly linear stability results, we then establish the local-in-time existence and nonlinear stability of current- vortex sheets by a suitable Nash-Moser iteration, provided the stability condition is satisfied at each point of the initial discontinuity. This result gives a new confirmation of the stabilizing effect of sufficiently strong magnetic fields on Kelvin-Helmholtz instabilities. This is a joint work with A. Morando (Brescia), P.Secchi(Brescia) and D. Yuan (Beijing Normal Univ.).