Stochastic transport equation with singular drift

Abstract

We prove existence, uniqueness and Sobolev regularity of weak solution of the Cauchy problem of the stochastic transport equation with drift in a large class of singular vector fields containing, in particular, the $L^d$ class, the weak $L^d$ class, as well as some vector fields that are not even in $L_{\mathrm{loc}}^{2+\epsilon }$ for any $\epsilon >0$.

References in corpus (2)

• Well-posedness by noise for scalar conservation laws
• On time inhomogeneous stochastic Itô equations with drift in $L_{d+1}$