Well-posedness of the 3D Stochastic Generalized Rotating Magnetohydrodynamics Equations

Authors : Mohamed TOUMLİLİN, Muhammad ZAİN ALABİDİN

Pages : 513-527

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Publication Date : 2022-12-30

Article Type : Research Paper

Abstract :In this paper we treat the 3D stochastic incompressible generalized rotating magnetohydrodynamics equations. By using littlewood-Paley decomposition and Itô integral, we establish the global well-posedness result for small initial data $insert ignore into journalissuearticles values(u_{0}, b_{0});$ belonging in the critical Fourier-Besov-Morrey spaces $\\mathcal{F\\dot{N}}_{2,\\lambda,q}^{\\frac{5}{2}-2 \\alpha +\\frac{\\lambda}{2}}insert ignore into journalissuearticles values(\\mathbb{R}^{3});$. In addition, the proof of local existence is also founded on a priori estimates of the stochastic parabolic equation and the iterative contraction method.
Keywords : Stochastic magnetohydrodynamics equation, well posedness, Fourier Besov Morrey spaces