Stochastic transport equation in bounded domains

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 Itô's formulation for bounded domains.Moreover, the uniqueness of weak solutions is obtained under suitable conditions.

We introduced several changes with respect to the first version

References in corpus (2)

• Noise Prevents Singularities in Linear Transport Equations
• A stochastic-Lagrangian approach to the Navier--Stokes equations in domains with boundary

Cited by in corpus (1)

• Wellposedness for stochastic continuity equations with Ladyzhenskaya-Prodi-Serrin condition