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

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

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

Copyright © 1999 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.