On a class of stochastic transport equations for L2loc vector fields

TL;DR

This paper investigates the existence and uniqueness of solutions to stochastic transport equations with irregular coefficients, relaxing regularity conditions while maintaining solution uniqueness.

Contribution

It introduces weaker integrability conditions on coefficients and initial data, ensuring solution uniqueness in stochastic transport equations.

Findings

Established existence of solutions under minimal regularity assumptions.

Proved uniqueness with only bounded divergence of coefficients.

Lowered regularity requirements compared to previous results.

Abstract

We study in this article the existence and uniqueness of solutions to a class of stochastic transport equations with irregular coefficients. Asking only boundedness of the divergence of the coefficients (a classical condition in both the deterministic and stochastic setting), we can lower the integrability regularity required in known results on the coefficients themselves and on the initial condition, and still prove uniqueness of solutions.