具有输运噪声和湍流压力的随机原始方程
The stochastic primitive equations with transport noise and turbulent pressure
摘要：
本文考虑了具有输运噪声和湍流压力的地球物理流的随机原始方程。利用随机最大$L^2$ -正则性、随机发展方程的临界空间理论和全局先验界，证明了该随机偏微分方程在非常粗糙的噪声项下解的整体存在唯一性.与这方面的其他结果相比，我们不需要对直接作用于速度场的输运噪声作任何小的假设，而且我们也允许更粗糙的噪声项。适应Stratonovich型噪声，更一般地说，可变粘度和/或电导率进行了讨论。
英文摘要：
In this paper we consider the stochastic primitive equation for geophysical flows subject to transport noise and turbulent pressure. Admitting very rough noise terms, the global existence and uniqueness of solutions to this stochastic partial differential equation are proven using stochastic maximal $L^2$-regularity, the theory of critical spaces for stochastic evolution equations, and global a priori bounds. Compared to other results in this direction, we do not need any smallness assumption on the transport noise which acts directly on the velocity field and we also allow rougher noise terms. The adaptation to Stratonovich type noise and, more generally, to variable viscosity and/or conductivity are discussed as well.
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