The global well-posedness of strong solutions to 2D MHD equations in Lei-Lin space

TL;DR

This paper proves the global existence and uniqueness of strong solutions to the 2D incompressible MHD equations in Lei-Lin space, expanding understanding of their well-posedness with initial data in specific functional spaces.

Contribution

It establishes the global well-posedness and uniqueness of strong solutions to 2D MHD equations in Lei-Lin space, a novel functional setting for this problem.

Findings

Global well-posedness of strong solutions in Lei-Lin space

Uniqueness of solutions in Lei-Lin space and L^2 space

Solutions exist for initial data in the intersection of Lei-Lin space and L^2

Abstract

In this paper, we study the Cauchy problem of the 2D incompressible magnetohydrodynamic equations in Lei-Lin space. The global well-posedness of a strong solution in the Lei-Lin space $\chi^{-1}(\mathbb{R}^2)$ with any initial data in $\chi^{-1}(\mathbb{R}^2)\cap L^2(\mathbb{R}^2)$ is established. Furthermore, the uniqueness of the strong solution in $\chi^{-1}(\mathbb{R}^2)$ and the Leray-Hopf weak solution in $L^2(\mathbb{R}^2)$ is proved.