Blowup of classical solutions for two-dimensional transverse magnetohydrodynamic equations

Abstract

In this paper, we investigate the blowup phenomenon of solutions for two-dimensional transverse magnetohydrodynamic (MHD) equations. By using the integration method, we first prove that the classical solutions for $\gamma \ge 2$ of the transverse MHD equations with the initial bounded region $\Omega \left(0\right)$ surrounded by vacuum will blow up in finite time. Furthermore, we also establish the finite-time singularity formation of the classical solutions for $\gamma >1$ to the transverse MHD equations with a class of non-vacuum initial values.