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
DOI: 10.12677/AAM.2023.127322, PDF,    科研立项经费支持
作者: 但园园：广东财经大学统计与数学学院，广东 广州
关键词: 全局解；不可压缩的MHD方程组；真空；Global Solution； Incompressible MHD Equations； Vacuum
摘要: 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。
Abstract: 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.
文章引用：但园园. 二维带真空的不可压缩MHD方程组的全局适定性[J]. 应用数学进展, 2023, 12(7): 3225-3239. https://doi.org/10.12677/AAM.2023.127322

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