In this article, we consider 2D stochastic primitive equations (PEs) driven by affine-linear multiplicative white noise and with random initial conditions. We obtain the global well-posedness of the stochastic PEs when the random initial condition satisfies sufficient Malliavin regularity. In the proof process of the global existence of solutions to 2D stochastic PEs, the Malliavin calculus plays a key role.

中文翻译：

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具有随机初始条件的随机二维原始方程的整体适定性

在本文中，我们考虑由仿射线性乘性白噪声驱动并具有随机初始条件的二维随机原始方程（PE）。当随机初始条件满足足够的Malliavin规律性时，我们获得了随机PE的全局适定性。在二维随机PE解决方案的全球存在的证明过程中，Malliavin演算起着关键作用。