About MHD system with small parameter

Article type: Research Article

Authors: Benameur, J. | Ghazel, M. | Majdoub, M.^;

Affiliations: Institut Préparatoire aux etudes d'Ingénieurs de Monastir, Tunisie E‐mail: jamel.benameur@ipest.rnu.tn | Institut préparatoire aux études d'ingenieurs de Sfax, Tunisie E‐mail: malek.ghazel@ipeis.rnu.tn | Faculté des Sciences de Tunis, Département de Mathématiques, Campus universitaire 1060, Tunis, Tunisie E‐mail: mohamed.majdoub@fst.rnu.tn

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Abstract: In this paper, we study the convergence of strong solutions of a MHD system. The proofs, in booth cases of ${\mathbb{T}}^{3}$ or ${\mathbb{R}}^{3}$, are based on spectral properties of the penalized operator and the energy method. Moreover, in the case of the whole space, we prove a refined convergence result for initial data 2D + 3D.

Journal: Asymptotic Analysis, vol. 41, no. 1, pp. 1-21, 2005