Sobolev differentiable stochastic flows for SDEs with singular coefficients: Applications to the transport equation

Salah-Eldin A. Mohammed, Torstein K. Nilssen, Frank N. Proske

In this paper, we establish the existence of a stochastic flow of Sobolev diffeomorphisms \[\mathbb{R}^d\ni x\quad\longmapsto\quadϕ_{s,t}(x)\in \mathbb{R}^d,\qquad s,t\in\mathbb{R}…