分析和PDE讨论班-Large time behavior of solutions to 3-D MHD system with initial data near equilibrium
主 题: 分析和PDE讨论班-Large time behavior of solutions to 3-D MHD system with initial data near equilibrium
报告人: 邓雯 (中科院数学研究所)
时 间: 2017-02-28 10:30-11:30
地 点: 理科1号楼1303
Abstract: It was conjectured by Califano and Chiuderi that the energy of incompressible MHD system is dissipated at a rate that is independent of the ohmic resistivity. We justify mathematically this conjecture in 3D provided that the initial magnetic field and velocity is a small perturbation of the equilibrium state $(e_3,0)$. We prove that for such data, 3-D incompressible MHD system without magnetic diffusion has a unique global solution. The velocity field and the difference between the magnetic field and $e_3$ decay to zero in both $L^\infty$ and $L^2$ norms and explicit rates are given. This is a joint work with P. Zhang.