Abstract The incompressible magnetohydrodynamic equations driven by additive fractional Brownian motions are considered. We firstly establish the local existence and uniqueness of the mild solution in L p space on a smooth bounded domain in R d ( d = 2 , 3 ) . The proof is based on the semigroup theory, fixed point theorem and the results of stochastic PDEs of linear parabolic type. In the proof, the eigenvalue problem with perfectly conducting wall condition is considered to weaken the requirements of noise terms. Finally, the global existence of mild solutions is also established by energy estimate.

中文翻译：

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由分数布朗运动驱动的随机 MHD 方程的温和解

摘要 考虑了由加性分数布朗运动驱动的不可压缩磁流体动力学方程。我们首先在R d (d = 2, 3)的光滑有界域上建立L p 空间中温和解的局部存在唯一性。证明基于半群论、不动点定理和线性抛物型随机偏微分方程的结果。在证明中，完美传导壁条件的特征值问题被认为弱化了噪声项的要求。最后，通过能量估计也建立了温和解的全局存在性。