International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Issue 4, Pages 28704, 19 p.
doi:10.1155/IJMMS/2006/28704
Convergence results for MHD system
Ridha Selmi
Département de Mathématiques, Institut Supérieur d'Informatique, Université de Tunis El-Manar, 2 rue Abou Rayhane Bayrouni, l'Ariana 2080, Tunisia
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.