主讲人：张挺 教授（浙江大学数学系）

时  间：2014年3月14日（周五）16:00-17:00

地  点：必赢76net线路官网北二区教学楼 510 教室

摘  要: In this talk, we consider the global existence and uniqueness of the solutions to the viscous, non-resistive MHD system. First, we provide a much simplified proof of the main result in [Lin, Zhang, Comm. Pure Appl. Math. 2014] concerning the global existence and uniqueness of smooth solutions to the Cauchy problem for a 3D incompressible complex fluid model under the assumption that the initial data are close to some equilibrium states. Beside the classical energy method, the interpolating inequalities and the algebraic structure of the equations coming from the incompressibility of the fluid are crucial in our arguments. We combine the energy estimates with the $L^\infty$ estimates for time slices to deduce the key $L^1$ in time estimates. The latter is responsible for the global in time existence. Second, we can obtain the similar result for 2D the incompressible viscous, non-resistive MHD system under the assumption that the initial data are close to some equilibrium states. At last, using the idea from Bardos, Sulem and Sulem [Trans. Amer. Math. Soc. 1988], for any initial data, we can obtain the global strong solutions when the background magnetic field is sufficiently large.