School of Mathematical Sciences Academic Report [2025] No. 014

(High-Level University Construction Series Report No. 1037)

Lecture Title: Global Solvability of Large Solutions to the Three-Dimensional Incompressible and Compressible MHD Equations with Density-Dependent Viscosities

Speaker: Fan Jie (Postdoctoral Researcher, Academy of Mathematics and Systems Science, Chinese Academy of Sciences)

Date & Time: 3:00–4:00 PM, March 21, 2025  

Venue: Room 514, Huixing Building, Shenzhen University  

Abstract: This talk not only investigates the Dirichlet problem of three-dimensional non-homogeneous incompressible MHD equations with density-dependent viscosity but also examines the Cauchy problem for the three-dimensional isentropic compressible magnetohydrodynamic equations with density-dependent viscosities. We prove that strong solutions exist globally provided that the initial density is large enough. These results generalize previous classical findings, which required solutions to have small perturbations from the resting state.  

Biography: Fan Jie received her Ph.D. from Capital Normal University and is currently a Special Research Assistant (Postdoctoral Researcher) at the Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences. Her research focuses on the global well-posedness theory and regularity criteria for compressible fluid equations. She has published four first-author papers in journals such as J. Math. Phys.、J. Math. Fluid Mech.、Nonlinear Anal. Real World Appl.、Discrete Contin. Dyn. Syst.  

All faculty and students are welcome to attend!

Invited by: Duan Qin

School of Mathematical Sciences  

March 17, 2025