Dissipative 2D MHD equations with L^1 vorticity and magnetic current

Abstract

We consider the two-dimensional (2D) Magneto-HydroDynamics (MHD) equations describing the evolution of a viscous incompressible electrically conducting fluid. In this paper, adopting the vorticity-current formulation and assuming that the initial fluid vorticity and magnetic current are in L1(ℝ2), we prove the local in-time existence and regularity of the solutions.