On the 3-D stochastic magnetohydrodynamic-α model

Gabriel Deugoué, Paul André Razafimandimby and Mamadou Sango

Stochastic Processes and their Applications, 2012, vol. 122, issue 5, 2211-2248

Abstract: We consider the stochastic three dimensional magnetohydrodynamic-α model (MHD-α) 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-α model to the stochastic 3D magnetohydrodynamic equations by proving a convergence theorem, that is, as the length scale α tends to zero, a subsequence of weak martingale solutions of the stochastic 3D MHD-α model converges to a certain weak martingale solution of the stochastic 3D magnetohydrodynamic equations. Finally, we prove the existence and uniqueness of the probabilistic strong solution of the 3D MHD-α under strong assumptions on the external forces.

Keywords: Magnetohydrodynamic; Martingale solution; Navier–Stokes-α; Compactness method; Tightness (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1016/j.spa.2012.03.002

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