Formation of Singularity for Full Compressible Magnetohydrodynamic Equations with Zero Resistivity in Two Dimensional Bounded Domains

Abstract

We are concerned with singularity formation of strong solutions to the two-dimensional (2D) full compressible magnetohydrodynamic equations with zero resistivity in a bounded domain. By energy method and critical Sobolev inequalities of logarithmic type, we show that the strong solution exists globally if the temporal integral of the maximum norm of the deformation tensor is bounded. Our result is the same as Ponce’s criterion for 3D incompressible Euler equations. In particular, it is independent of the magnetic field and temperature. Additionally, the initial vacuum states are allowed.