International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Article ID 28704, 19 pages
doi:10.1155/IJMMS/2006/28704
Convergence results for MHD system
1Département de Mathématiques, Institut Supérieur d'Informatique, Université de Tunis El-Manar, 2 rue Abou Rayhane Bayrouni, l'Ariana 2080, Tunisia
2Laboratoire des Equations aux Derivées Partielles et Applications, Faculté des Sciences de Tunis, Compus Universitaire, Tunis 2092, Tunisia
Received 14 April 2005; Revised 29 September 2005; Accepted 26 January 2006
Dedicated to Mouna
Copyright © 2006 Ridha Selmi. 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
A magnetohydrodynamic system is investigated in
both cases of the periodic domain T3 and the whole space R3. Existence and uniqueness of strong solution are proved. Asymptotic
behavior of the solution when the Rossby number ε goes to zero is studied. The proofs use the spectral properties of
the penalization operator and involve Friedrich's method,
Schochet's methods, and product laws in Sobolev spaces of
sufficiently large exponents.