We show that the stochastic 3D primitive equations with the Neumann boundary condition on the top, the lateral Dirichlet boundary condition and either the Dirichlet or the Neumann boundary condition on the bottom driven by multiplicative gradient-dependent white noise have unique maximal strong solutions both in the stochastic and PDE senses under certain assumptions on the growth of the noise. For the case of the Neumann boundary condition on the bottom, global existence is established by using the decomposition of the vertical velocity to the barotropic and baroclinic modes and an iterated stopping time argument. An explicit example of non-trivial infinite dimensional noise depending on the vertical average of the horizontal gradient of horizontal velocity is presented.

我们表明，由乘法梯度相关白噪声驱动的顶部为 Neumann 边界条件、横向 Dirichlet 边界条件以及底部为 Dirichlet 或 Neumann 边界条件的随机 3D 原始方程在在噪声增长的某些假设下的随机和 PDE 感觉。对于底部的 Neumann 边界条件，通过使用垂直速度分解为正压和斜压模式以及迭代停止时间参数来建立全局存在性。给出了一个依赖于水平速度水平梯度的垂直平均值的非平凡无限维噪声的明确例子。