Flows for non-smooth vector fields with subexponentially integrable divergence

Abstract

In this paper, we study flows associated to Sobolev vector fields with subexponentially integrable divergence. Our approach is based on the transport equation following DiPerna-Lions [DPL89]. A key ingredient is to use a quantitative estimate of solutions to the Cauchy problem of transport equation to obtain the regularity of density functions.

24 pages, revised