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