中国科学院数学与系统科学研究院

数学研究所

数学科学全国重点实验室

学术报告

偏微分方程研讨班

Speaker: 徐鑫 副教授 （中国海洋大学）

Inviter: 郝成春

Language: Chinese

Title:Stabilizing effect of the magnetic field to the singular limits of 

compressible MHD system

Time&Venue: 2025年7月3日（星期四）15:00-16:00

& 南楼N514

Abstract:Due to the formation of boundary layers, singular limit problems of 

fluid dynamic equations with physical boundaries are difficult to study in 

general. For example, the low Mach number limit of Navier-Stokes equation 

with Dirichlet boundary condition remains an open problem in classical 

solution setting. In this talk, we will show that appropriate background 

magnetic field may have some stabilizing effect to the boundary layers. In 

certain cases, high-order uniform estimates of the solutions can be 

established.rity and finite-time singularity in these models. We also revisit 

Elgindi's result on 2D Loglog-Euler type equations to give a complete and 

slightly different proof.

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Speaker: 琚强昌 研究员

（北京应用物理与计算数学研究所）

Inviter: 郝成春

Language: Chinese

Title:The global existence and low Mach number limit for full Navier-Stokes 

equations around the Couette flow

Time&Venue: 2025年7月3日（星期四）16:00-17:00

& 南楼N514

Abstract: We study the global existence and low Mach number limit of strong 

solutions to the 2-D full compressible Navier-Stokes equations around the 

plane Couette flow with non-slip and isothermal boundary conditions. It is 

shown that the plane Couette flow is asymptotically stable for sufffciently 

small initial perturbations, provided that the Reynolds number, Mach number 

and temperature difference between the top and the lower walls are small. For 

the case that both the top and the lower walls maintain the same temperature, 

we further prove that such global strong solutions converge to a steady solution 

of the incompressible Navier-Stokes equations as the Mach number goes to 

zero.