$L^p-$solutions of the stochastic transport equation

Abstract

We consider the stochastic transport linear equation and we prove existence and uniqueness of weak $L^p-$solutions. Moreover, we obtain a representation of the general solution and a Wong-Zakai principle for this equation. We make only minimal assumptions, similar to the deterministic problem. The proof is supported on the generalized Itô-Ventzel-Kunita formula (see 15) and the theory of Lions-DiPerna on transport linear equation (see 9).

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