Well-posedness of the stochastic transport equation with unbounded drift

TL;DR

This paper establishes the well-posedness of the stochastic transport equation with unbounded drift, demonstrating existence, uniqueness, and stability of solutions using stochastic analysis techniques.

Contribution

It provides new results on the well-posedness of stochastic transport equations with unbounded, Holder continuous drifts, expanding theoretical understanding.

Findings

Existence of solutions under Holder continuous drift.

Uniqueness of solutions for the stochastic transport equation.

Strong stability results for solutions.

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.