报告题目：Stabilizing Effect of the Magnetic Field on 2D Magnetohydrodynamic Flow

报告人：张剑文（厦门大学数学科学学院，教授）

报告时间：6月1号(周三)下午15：30—17：00

报告地点：腾讯会议ID：221-730-207

校内联系人：王金环 刘生全

报告摘要：This paper intends to study an experimentally observed stabilizing phenomenon and to prove a mathematically rigorous stability result on the perturbations near a background magnetic field. Physical experiments and numerical simulations have observed a remarkable phenomenon that a background magnetic field can smooth and stabilize the electrically conducting turbulent fluids. To understand the mechanism of this phenomenon, we focus on a special 2D magnetohydrodynamic (MHD) system with anisotropic dissipation and partial damping and examine the stability near a background magnetic field. Due to the lack of full dissipation and damping, this stability problem is not trivial. Without the presence of a magnetic field, the fluid velocity is governed by the 2D Navier--Stokes equations in the whole space $\mathbb R^2$ with only vertical dissipation, and its stability (near the trivial solution) is still an open problem. However, when coupled to the magnetic field in such an MHD system, we are able to show that any perturbation near a background magnetic field is globally stable in Sobolev space $H^2$. This result reflects the observed stabilizing effect of the magnetic field. 

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