题 目：Global uniform regularity for the 3D incompressible MHD equations with slip boundary condition near an equilibrium
内容简介：This paper solves the global conormal regularity problem for the three-dimensional incompressible MHD equations with slip boundary condition near a background magnetic field. Motivated by applications in geophysics, the MHD system considered here is anisotropic with small vertical dissipation and small horizontal magnetic diffusion. By exploiting the enhanced dissipation due to the background magnetic field and introducing three layers of energy functionals, we are able to establish global-in-time uniform bounds that are independent of vertical viscosity and horizontal resistivity. These global conormal regularity estimates allow us to pass to the limit and obtain the convergence to the MHD system with no vertical dissipation and horizontal magnetic diffusion. In the special case of the 3D incompressible Navier-Stokes, explicit long-time rates are also extracted in the zero vertical viscosity limit.
报告人：高金城
报告人简介：中山大学博士研究生导师（逸仙学者），获得科技部重点研发青年科学家项目和广东特支计划青年拔尖人才项目等资助，主要从而流体力学相关方程的理论与应用研究，在时间衰减估计、适定性和粘性消失极限方程取得了一些好的成果。
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信息科学技术学院
2024年10月21日