Global regularity of the two-dimensional regularized MHD equations

TL;DR

This paper proves the global regularity of classical solutions to the 2D regularized MHD equations with minimal dissipation, advancing understanding of their long-term behavior.

Contribution

It establishes the global regularity of solutions for 2D regularized MHD equations with minimal dissipation, improving upon previous results.

Findings

Proved global regularity of classical solutions.

Achieved results with minimal dissipation assumptions.

Improved upon previous regularity results.

Abstract

In this paper, we consider the Cauchy problem of the two-dimensional regularized incompressible magnetohydrodynamics equations. The main objective of this paper is to establish the global regularity of classical solutions of the magnetohydrodynamics equations with the minimal dissipation. Consequently, our results significantly improve the previous works.