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International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Article ID 28704, 19 pages

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

Copyright © 2006 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.


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.