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 global well-posedness of both problems with suitable boundary conditions around the equilibrium is established, and the solutions are shown to decay almost exponentially to the equilibrium. The results reveal the strong stabilizing effects of the transversal magnetic field. One of the key observations here is an induced damping structure for the fluid vorticity due to the resistivity and the transversality of the magnetic field. This is a joint work with Yanjin Wang.
Professor Zhouping Xin is an expert in the areas of partial differential equations, mathematical physics, fluid mechanics, nonlinear waves, numerical analysis and numerical methods for PDEs and applied mathematics. He has made substantial contributions to the stability theory linear and nonlinear waves, boundary layer theory, multi-dimensional shock wave theory, vortex methods and relaxation methods, transonic flows, and Navier-Stokes systems. After got his Ph.D in mathematics from the University of Michigan (Ann Arbor) in 1988, Professor Xin joined The Courant Institute of Mathematical Sciences at New York University first as a Courant Instructor, where he became a full professor of mathematics in 1995. In 2001, Professor Xin moved from the New York University to The Chinese University of Hong Kong where he has been the William M. W. Mong Professor of Mathematics until now. Currently Professor Zhouping Xin is the Executive Director of the Institute of Mathematical Sciences at The Chinese University of Hong Kong. Professor Xin got many honors including: Sloan Research Fellow (1991-1993, USA), Presidential Fellow (1993, USA); ICM invited speaker (2002); and Morningside Gold Medalist in Mathematics (2004). Professor Xin is the co-editor-in-chief of MAA, associated editor of JMP and M2AS, and member of the editorial boards for many journals such as M3AS, Kyoto J. Math., and Sciences China Mathematics, etc.
Institute of Natural Sciences, Shanghai Jiao Tong University
Ministry of Education Key Lab in Scientific and Engineering Computing
Shanghai Center for Applied Mathematics (SJTU Center)