Existence of global solution for a differential system with initial data in Lp

Abstract

In this paper, we study the system governing flows in the magnetic field within the earth. The system is similar to the magnetohydrodynamic (MHD) equations. By establishing a new priori estimates and following Calderón's procedure for the Navier Stokes equations [1], we obtained, for initial data in space Lp, the global in time existence and uniqueness of weak solution of the system subject to appropriate conditions.