A Remark On Global Regularity of 2D Generalized Magnetohydrodynamic Equations

Abstract

In this paper we study the global regularity of the following 2D (two-dimensional) generalized magnetohydrodynamic equations \begin{eqnarray*} \left\{\begin{array}{llll} u_t + u \cdot \nabla u & = & - \nabla p + b \cdot \nabla b - ν(-\triangle)^α u b_t + u \cdot \nabla b & = & b \cdot \nabla u - κ(-\triangle)^β b \end{array}\right. \end{eqnarray*} and get global regular solutions when $ 0\leqslantα< 1 / 2,\,\, β\geqslant 1, \,\,3α+ 2β>3 $, which improves the results in \cite{TYZ2013}. In particular, we obtain the global regularity of the 2D generalized MHD when $α=0$ and $β>\frac 32$.

9 pages