On the 3-D stochastic magnetohydrodynamic-α model

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Authors

Deugoue, Gabriel
Razafimandimby, Paul Andre
Sango, Mamadou

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Elsevier

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.

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Keywords

Martingale solution, Compactness method, Tightness, Magnetohydrodynamic-αα model (MHD-αα), Magnetohydrodynamic (MHD), Navier–Stokes equations (NSE), Navier–Stokes-αα model

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Citation

Deugoue, G, Razafimandimby, PA & Sango, M 2012, 'On the 3-D stochastic magnetohydrodynamic-α model', Stochastic Processes and Their Applications, vol. 122, no. 5, pp. 2211-2248.