Abstract: In this talk, I shall introduce some recent results on global (or small) solutions of the incompressible magnetohydrodynamic(MHD) system with some kinds of dissipation terms in 2D，including the fractional Laplacian, anisotropic dissipation. These results established the global existence and uniqueness of smooth solutions when the initial data is close to an equilibrium state. Some of results presented rigorously confirm a nonlinear phenomenon observed in physical experiments that the magnetic field stabilizes electrically conducting fluids in fact, and some cases also gave the explicit large-time decay rates for various Sobolev norms of the solutions.

个人简介：

许孝精，男，北京师范大学数学科学学院教授，博士生导师，副院长。2005年于吉林大学获得博士学位。主要从事来自流体动力学中的偏微分方程组适定性理论的研究，已经完成学术论文50余篇。近期主要讨论了Navier-Stokes方程、Boussinesq方程、MHD方程等在不同情形的耗散效应下对相应问题整体适定性的影响。