International Journal of Mathematics and Mathematical Sciences 
Volume 22 (1999), Issue 4, Pages 823-834
doi:10.1155/S0161171299228232

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

Peter Bates,1 Fengxin Chen,1 and Ping Wang2

 1Department of Mathematics, Brigham Young University, Provo 84602, Utah, USA
2Department of Mathematics, Penn State University, Schuylkill Hven 17972, PA, USA
Received 15 October 1997

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.