© 2016 Elsevier Inc. 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 . 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.
|Journal||Journal of Differential Equations|
|Publication status||Published - 15 Jul 2016|
- Non-smooth flow
- Sobolev vector fields
- Transport equation