走向现代数学学术报告 - 许孝精教授（No. 970)

报告题目：Global Stability of 3D Compressible Non-Resistive MHD: Hidden Damping and Rational Background Fields

报 告 人：许孝精 教授（北京师范大学）

邀 请 人：李心亮 博士

报告时间：2026年10月15日 14：30

报告地点：东海岸校区D209

报告摘要：In this talk, we shall introduce the global well-posedness and nonlinear stability of classical solutions to the three-dimensional compressible viscous, non-resistive MHD system on T^3 near the equilibrium (1,0,e_3), for small x_3-symmetric perturbations and without the Diophantine condition on the background magnetic field. The central obstruction is the x_3-independent sector, in which the density and the magnetic field possess no dissipation, no damping, and no decay, which are overcomed by exhibiting a hidden wave structure for the exact total pressure. Together with a damped wave structure for the oscillatory sector and space-time weighted energy functionals with shifted time weights, this yields global existence, uniform stability, and explicit polynomial decay rates. This is a joint work with Lin-An Li, Qian Li and Jiahong Wu.

报告人简介：许孝精，北京师范大学数学科学学院教授，博士生导师，数学建模教育中心执行主任。主要研究流体力学数学理论，给出了一系列Boussinesq方程的适定性理论。曾获“吉林省优秀博士学位论文”北京市优秀教学成果奖、北师大励耘优秀青年教师奖一等奖、校优秀博士生学位论文指导教师、校优质课程特等奖等。主持了多项国家自然科学基金，发表学术论文60余篇，被引用1067余次，大部分成果发表在Math.Ann., J.Math.Pures Appl., J.Funct. Anal., SIAM J. Math. Anal., Indiana Univ.Math.J等国际知名学术期刊。曾在法国、美国、加拿大、波兰和香港等地区进行学术访问10余次。