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Initial-boundary value problem for stochastic transport equations
Stochastics and Partial Differential Equations: Analysis and Computations ( IF 1.5 ) Pub Date : 2020-09-07 , DOI: 10.1007/s40072-020-00180-9
Wladimir Neves , Christian Olivera

This paper concerns the Dirichlet initial-boundary value problem for stochastic transport equations with non-regular coefficients. First, the existence and uniqueness of the strong stochastic traces is proved. The existence of weak solutions relies on the strong stochastic traces, and also on the passage from the Stratonovich into Itô’s formulation for bounded domains. Moreover, the uniqueness is established without the divergence of the drift vector field bounded from below.



中文翻译:

随机运输方程的初边值问题

本文涉及具有非正则系数的随机运输方程的Dirichlet初边值问题。首先,证明了强随机痕迹的存在和唯一性。弱解的存在取决于强大的随机踪迹,也取决于Stratonovich进入Itô的有界域公式。而且,建立唯一性而没有从下面限制的漂移矢量场的发散。

更新日期:2020-09-08
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