English

Stochastic transport equation with bounded and Dini continuous drift

Probability 2021-07-29 v2

Abstract

The results established by Flandoli, Gubinelli and Priola ({\it Invent. Math.} {\bf 180} (2010) 1--53) for stochastic transport equation with bounded and H\"{o}lder continuous drift are generalized to bounded and Dini continuous drift. The uniqueness of LL^\infty-solutions is established by the It\^o--Tanaka trick partially solving the uniqueness problem, which is still open, for stochastic transport equation with only bounded measurable drift. Moreover the existence and uniqueness of stochastic diffeomorphisms flows for a stochastic differential equation with bounded and Dini continuous drift is obtained.

Cite

@article{arxiv.2105.08465,
  title  = {Stochastic transport equation with bounded and Dini continuous drift},
  author = {Jinlong Wei and Guangying Lv and Wei Wang},
  journal= {arXiv preprint arXiv:2105.08465},
  year   = {2021}
}

Comments

39pages

R2 v1 2026-06-24T02:13:14.802Z