Speaker: Wu Jiahong, professor, University of Notre Dame

Date: July 14, 2025

Time: 14:30-15:30 pm

Location: B1032, Zhixin Building, Shandong University

Sponsor: School of Mathematics, Shandong University

Abstract:

Physical experiments and numerical simulations have revealed a remarkable stabilizing effect of magnetic fields: they can smooth and suppress instabilities in electrically conducting fluids. This phenomenon has motivated extensive research into the underlying mechanisms within the framework of the magnetohydrodynamics (MHD) equations. In this talk, I will present recent results on the nonlinear stability and long-time behavior of compressible MHD systems with anisotropic dissipation. In particular, I will discuss three settings: (1) the three-dimensional compressible non-resistive MHD equations near a background magnetic field satisfying a Diophantine condition; (2) the three-dimensional non-isentropic MHD equations with no velocity dissipation; and (3) the compressible MHD equations with horizontal magnetic diffusion near a general constant magnetic field. These results reveal a rich wave structure and uncover stabilizing mechanisms unique to compressible flows—phenomena that do not appear in the incompressible case.

For more information, please visit:

https://www.view.sdu.edu.cn/info/1020/204394.htm