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Free Interface Problems for The Incompressible Inviscid Resistive MHD

发布时间:2022-07-06 作者: 浏览次数:
Speaker: 辛周平 DateTime: 2022年7月6日(周三)下午4:00—5:00
Brief Introduction to Speaker:

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。1988年获美国密歇根大学博士学位,后加入美国纽约大学柯朗数学研究所并于1996年成为终身教授。辛周平教授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突出贡献。他曾任香港数学会会长,获得的许多荣誉包括:世界华人数学家大会“晨兴数学奖金奖”(2004年)、国际数学家大会特邀报告人(2002年)、美国“Sloan奖”(1991年)等。

 

Place: 六号楼6401
Abstract:In this talk I will discuss the global well-posedness of free interface problems for the incompressible inviscid resistive MHD. Both plasma-vacuum and plasma-plasma interface problems in a horizontally periodic slab impressed by a uniform transversal magnetic field will be studied. The free boundary value problems with suitable physical boundary conditions will be formulated and the global well-posedness of both problems with surface tension around the equilibrium is established. Furthermore, the solutions are shown to decay almost exponentially to the equilibrium. Since the global well-posedness of the free-boundary problems for the incompressible ideal Euler equations with/or without surface tension around the equilibrium is unknown, our results here reveal the strong stabilizing effects of the transversal magnetic field and resistivity. Indeed, one of the key observations here is an induced damping structure for the fluid vorticity due to the resistivity and the transversal...