Global Regularity of the Logarithmically Supercritical MHD System in Two-Dimensional Space

Abstract

In this paper, we study the global regularity of logarithmically supercritical MHD equations in $2$ dimensional, in which the dissipation terms are $-\mu\Lambda^{2\alpha}u$ and $-\nu\mathcal{L}^{2\beta} b$. We show that global regular solutions in the cases $0<\alpha<\frac{1}{2}, β > 1, 3α + 2β > 3$.