- Advances in the Theory of Nonlinear Analysis and its Application
- Vol: 6 Issue: 4
- Well-posedness of the 3D Stochastic Generalized Rotating Magnetohydrodynamics Equations
Well-posedness of the 3D Stochastic Generalized Rotating Magnetohydrodynamics Equations
Authors : Mohamed Toumlilin, Muhammad Zain Al-abidin
Pages : 513-527
View : 4 | Download : 2
Publication Date : 2022-12-30
Article Type : Research
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 $(u_{0}, b_{0})$ belonging in the critical Fourier-Besov-Morrey spaces $\\mathcal{F\\dot{N}}_{2,\\lambda,q}^{\\frac{5}{2}-2 \\alpha +\\frac{\\lambda}{2}}(\\mathbb{R}^{3})$. 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