Initial-boundary value problem for stochastic transport equations

Abstract

This paper concerns the Dirichlet initial-boundary value problem for stochastic transport equations with non-regular coefficients. First, the existence and uniqueness of the strong stochastic traces is proved. The existence of weak solutions relies on the strong stochastic traces, and also on the passage from the Stratonovich into Ito’s formulation for bounded domains. Moreover, the uniqueness is established without the divergence of the drift vector field bounded from below.