English

Stochastic Lagrangian Flows for SDEs with rough coefficients

Probability 2025-05-01 v4 Analysis of PDEs

Abstract

We prove the existence and uniqueness of Stochastic Lagrangian Flows and almost everywhere Stochastic Flows for non-degenearted SDEs with rough coefficients. As an application of our main result, we show that there exists a unique Stochastic Flow corresponding to each Leray-Hopf solution of 3D Navier-Stokes equation in the DiPerna-Lions sense.

Keywords

Cite

@article{arxiv.1911.05562,
  title  = {Stochastic Lagrangian Flows for SDEs with rough coefficients},
  author = {Guohuan Zhao},
  journal= {arXiv preprint arXiv:1911.05562},
  year   = {2025}
}

Comments

Theorem 2.4 presents a result that is, to some extent, already known in the literature, and the proof of Theorem 5.1 contains some errors

R2 v1 2026-06-23T12:14:32.825Z