Zero-noise selection and Large Deviations in $L_t^{\infty }{L}_x^p$ for the stochastic transport equation beyond DiPerna-Lions

Gianluca Crippa, Eliseo Luongo, Umberto Pappalettera

We consider $L_t^{\infty }{L}_x^p$ solutions of the stochastic transport equation with drift in $L_t^{\infty }{W}_x^{1,q}$. We show strong existence and pathwise uniqueness of solutions in…