论文标题
带有传输噪声的3D随机原始方程的适合度
Well-Posedness of the 3D Stochastic Primitive Equations with Transport Noise
论文作者
论文摘要
我们表明，具有物理边界条件的随机3D原始方程或顶部和底部的neumann边界条件以及由多个梯度依赖的白噪声驱动的侧面的Dirichlet边界条件在噪声生长的某些假设下都具有随机和PDE的最大强大解决方案。对于后一种边界条件，使用基于垂直速度对压缩和斜视模式的参数建立了全局存在，并迭代了停止时间参数。提出了水平速度水平梯度的垂直平均值的非平凡无限尺寸噪声的明确示例。
We show that that the stochastic 3D primitive equations with either the physical boundary conditions or Neumann boundary conditions on the top and bottom and Dirichlet boundary condition on the sides driven by multiplicative gradient-dependent white noise have unique maximal strong solutions both in stochastic and PDE sense under certain assumptions on the growth of the noise. For the latter boundary conditions global existence is established using an argument based on decomposition of vertical velocity to 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.
