Remark on the global regularity of 2D MHD equations with almost Laplacian magnetic diffusion

TL;DR

This paper proves the global regularity of solutions to 2D incompressible MHD equations with almost Laplacian magnetic diffusion, advancing understanding of their well-posedness without velocity dissipation.

Contribution

It establishes the global regularity for 2D MHD equations with almost Laplacian magnetic diffusion, extending previous results and approaching the classical case.

Findings

Proves global regularity of solutions in the whole space.

Generalizes previous work on magnetic diffusion.

Brings the analysis closer to the classical Laplacian magnetic diffusion case.

Abstract

Whether or not the classical solutions of the two-dimensional (2D) incompressible magnetohydrodynamics (MHD) equations with only Laplacian magnetic diffusion (without velocity dissipation) are globally well-posed is a difficult problem and remains completely open. In this paper, we establish the global regularity of solutions to the 2D incompressible MHD equations with almost Laplacian magnetic diffusion in the whole space. This result can be regarded as a further improvement and generalization of the previous works. Consequently, our result is more closer to the resolution of the global regularity issue on the 2D MHD equations with standard Laplacian magnetic diffusion.