On the 3-D stochastic magnetohydrodynamic-α model

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:122

Article

Deugoue, Gabriel^1,2  Razafimandimby, Paul Andre¹  Sango, Mamadou¹ 

[1] Univ Pretoria, Dept Math & Appl Math, ZA-0002 Pretoria, South Africa

[2] Univ Dschang, Dept Math & Comp Sci, Dschang, Cameroon

关键词: Magnetohydrodynamic;    Martingale solution;    Navier-Stokes-alpha;    Compactness method;    Tightness;   

DOI  :  10.1016/j.spa.2012.03.002

来源: Elsevier

【 摘 要 】

We consider the stochastic three dimensional magnetohydrodynamic-alpha model (MHD-alpha) which arises in the modeling of turbulent flows of fluids and magnetofluids. We introduce a suitable notion of weak martingale solution and prove its existence. We also discuss the relation of the stochastic 3D MHD-alpha model to the stochastic 3D magnetohydrodynamic equations by proving a convergence theorem, that is, as the length scale alpha tends to zero, a subsequence of weak martingale solutions of the stochastic 3D MHD-alpha model converges to a certain weak martingale solution of the stochastic 3D magnetohydrodynarnic equations. Finally, we prove the existence and uniqueness of the probabilistic strong solution of the 3D MHD-alpha under strong assumptions on the external forces. (C) 2012 Elsevier By. All rights reserved.

【 授权许可】

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