报告题目：On Stabilizing Effects of Transversal Magnetic Fields on Interfacial Wave Motions

（横向磁场对界面波运动的稳定作用）

主讲人：辛周平教授（香港中文大学）

报告邀请人：孙怡东教授

报告时间：2022年9月24日上午9:00-10:00

报告地点：腾讯会议944337545

会议链接：https://meeting.tencent.com/dm/LYYI5ogKk3Uw

报告摘要：Dynamical interface motions are important flow patterns and fundamental free boundary problems in fluid mechanics. Such waves for purely inviscid fluids are subject to various instabilities such as Kelvin-Helmholtz and Rayleigh-Taylor instabilities unless other stabilizing effects such as surface tension, Taylor-sign conditions or dissipations are imposed. However, in the presence of magnetic fields, it has been known that tangential magnetic fields may have stabilizing effects for free surface waves such as plasma-vacuum or plasma-plasma interfaces (at least locally in time), yet whether transversal magnetic fields (which occurs often for interfacial waves for astrophysical plasmas) can stabilize typical free interfacial waves remains to be some open problems. In this talk I will show the stabilizing effects of the transversal magnetic fields for some interfacial waves for both compressible and incompressible multi-dimensional magnetohydrodynamics (MHD). First, I will present the local (in time) well-posedness in Sobolev space of multi-dimensional compressible MHD contact discontinuities, which are most typical interfacial waves for astrophysical plasma and prototypical fundamental waves for systems of hyperbolic conservations. Such waves are characteristic discontinuities for which there is no flow across the discontinuity surface while the magnetic field crosses transversally, which lead to a two-phase free boundary problem that may have nonlinear Rayleigh-Taylor instability and whose front symbols have no ellipticity. Second, I will discuss some results on the global well-posedness of free interface problems for the incompressible inviscid resistive MHD with transversal magnetic fields. Both plasma-vacuum and plasmaplasma interfaces are studied. The global in time well-posedness of both interface problems in a horizontally periodic slab impressed by a uniform non-horizontal magnetic field near an equilibrium are established, which reveal the strong stabilizing effect of the transversal field. This talk is based on joint works with Professor Yanjin Wang.

个人简历：辛周平，香港中文大学数学科学研究所常务所长、蒙民伟数学讲座教授，国际数学家大会（ICM）45 分钟特邀报告人，MAA 主编，JMP 和 M2AS副主编，M3AS、SCM、Kyoto J. of Math 等十几种杂志的编委或主编。长期从事流体力学偏微分方程理论研究，在双曲守恒律、高维激波、边界层理论、混合型方程、可压流体与不可压流体方程和松弛格式等领域做出了重要的具有国际影响的研究成果。至今发表论文 180 余篇，google 引用超 1 万 2 千余次，近 5 年 google 引用超 4 千次，是美国 Sloan Research Fellow。曾任香港数学会会长，曾获得美国 Sloan 研究奖、教育部长江讲座以及晨兴数学金奖。