二维带真空的不可压缩MHD方程组的全局适定性

Global Well-Posedness for the 2D Incompressible MHD Equations with Vacuum

本文主要研究了带有非负有界密度的二维不可压缩磁流体力学(MHD)方程组的全局适定性问题。对于初始密度没有正则性或者没有正下界或者没有兼容性条件时,我们通过使用一个全新的先验估计建立了不可压缩磁流体力学(MHD)方程组的全局解。本文结果推广了二维Navier-Stokes方程组在周期区域上的全局适定性结果。

This paper focuses on the global well-posedness for the 2D incompressible Magnetohydrodynamics (MHD) equations with only bounded nonnegative density. We establish the global solutions by using a new a prior estimate without regularity or positive lower bound for the initial density, or compat-ibility conditions. This result generalizes previous result for the 2D Navier-Stokes equations on the periodic domain.