This paper focuses on a system of the 2-D MHD equations with fractional kinematic dissipation and partial magnetic diffusion under random perturbations. We first establish the local existence, uniqueness and blow-up criterion of pathwise classical solution to the corresponding SPDE with general multiplicative noise in ${\mathbb{R}}^2$. Moreover, when the noise is non-autonomous and linear, we further establish global existence and large-time behavior of pathwise solutions by exploiting the structure of the equations and some estimates on Girsanov type stochastic processes.

中文翻译：

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具有分数运动耗散和部分磁扩散的随机MHD方程。 ${\mathbb{[R}}^{\mathrm{2个}}$

本文着重研究具有随机运动的分数运动耗散和部分磁扩散的二维MHD方程组。我们首先建立了具有一般乘性噪声的相应SPDE的路径经典解的局部存在性，唯一性和爆破准则。${\mathbb{[R}}^{\mathrm{2个}}$。此外，当噪声是非自治且线性的时，我们通过利用方程的结构和对Girsanov型随机过程的一些估计，进一步建立了路径解的整体存在性和长时间行为。