Well-posedness of the stochastic transport equation with unbounded drift

Abstract

The Cauchy problem for a multidimensional linear transport equation with unbounded drift is investigated. Provided the drift is Holder continuous , existence, uniqueness and strong stability of solutions are obtained. The proofs are based on a careful analysis of the associated stochastic flow of characteristics and techniques of stochastic analysis.

arXiv commentWe reformulated our results : we eliminated the section of renormalization. However, we introduce a new results. We present the existence, uniqueness and stability for the stochastic transport equation