Crisan Dan, Lang Oana
Department of Mathematics, Imperial College London, London, UK.
J Dyn Differ Equ. 2024;36(4):3175-3205. doi: 10.1007/s10884-022-10243-1. Epub 2023 Jan 20.
In this paper, we study the well-posedness properties of a stochastic rotating shallow water system. An inviscid version of this model has first been derived in Holm (Proc R Soc A 471:20140963, 2015) and the noise is chosen according to the Stochastic Advection by Lie Transport theory presented in Holm (Proc R Soc A 471:20140963, 2015). The system is perturbed by noise modulated by a function that is not Lipschitz in the norm where the well-posedness is sought. We show that the system admits a unique maximal solution which depends continuously on the initial condition. We also show that the interval of existence is strictly positive and the solution is global with positive probability.
在本文中，我们研究了一个随机旋转浅水系统的适定性性质。该模型的无粘版本最初由霍尔姆（《皇家学会学报A》471:20140963，2015）推导得出，并且噪声是根据霍尔姆（《皇家学会学报A》471:20140963，2015）中提出的李传输随机平流理论来选取的。该系统受到一个函数调制的噪声的扰动，该函数在所寻求适定性的范数下不是利普希茨连续的。我们证明该系统存在唯一的最大解，它连续依赖于初始条件。我们还证明存在区间严格为正，并且解以正概率全局存在。
