Stochastic transport equation in bounded domains
Analysis of PDEs
2020-09-07 v5 Probability
Abstract
This paper is concerned with the initial-boundary value problem \; for stochastic transport equations in bounded domains. For a given stochastic perturbation of the drift vector field, we prove existence and uniqueness of weak solutions with non-regular coefficients. The existence of weak solutions relies strongly on the existence of strong stochastic trace, and also on the passage from the Stratonovich into It\^o's formulation for bounded domains.Moreover, the uniqueness of weak solutions is obtained under suitable conditions.
Cite
@article{arxiv.1406.3735,
title = {Stochastic transport equation in bounded domains},
author = {Wladimir Neves and Christian Olivera},
journal= {arXiv preprint arXiv:1406.3735},
year = {2020}
}
Comments
We introduced several changes with respect to the first version