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

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.