In this paper we prove the existence and uniqueness of maximal strong (in PDEsense) solution to several stochastic hydrodynamical systems on unbounded andbounded domains of $mathbb{R}^n$, $n=2,3$. This maximal solution turns out tobe a global one in the case of 2D stochastic hydrodynamical systems. Ourframework is general in the sense that it allows us to solve the Navier-Stokesequations, MHD equations, Magnetic B'enard problems, Boussinesq model of theB'enard convection, Shell models of turbulence and the Leray-$lpha$ modelwith jump type perturbation. Our goal is achieved by proving general results about the existence ofmaximal and global solution to an abstract stochastic partial differentialequations with locally Lipschitz continuous coefficients. The method of theproofs are based on some truncation and fixed point methods.
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机译：在本文中，我们证明了$ mathbb {R} ^ n $，$ n = 2,3 $的无界和有界域上几个随机流体力学系统的最大强解（在PDEsense中）的存在和唯一性。在2D随机流体动力系统的情况下，这种最大解决方案变成了全局解决方案。从某种意义上说，我们的框架是通用的，它使我们能够解决Navier-Stokesequations，MHD方程，B'enard对流的Boussinesq模型，B'enard对流的Boussinesq模型，湍流的Shell模型以及带跳变的Leray-$ alpha $模型类型摄动。我们的目标是通过证明关于具有局部Lipschitz连续系数的抽象随机偏微分方程的最大和整体解的存在性的一般结果而实现的。证明方法基于一些截断和定点方法。
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