SDEs with critical time dependent drifts: strong solutions
Probability
2025-06-04 v5
Abstract
Based on a compactness criterion for random fields in Wiener-Sobolev spaces, in this paper, we prove the unique strong solvability of time-inhomogeneous stochastic differential equations with drift coefficients in critical Lebesgue spaces, which gives an affirmative answer to a longstanding open problem. As an application, we also prove a regularity criterion for solutions of a stochastic system proposed by Constantin and Iyer (Comm. Pure. Appl. Math. 61(3): 330-345, 2008), which is closely related to the Navier-Stokes equations.
Keywords
Cite
@article{arxiv.2103.05803,
title = {SDEs with critical time dependent drifts: strong solutions},
author = {Michael Röckner and Guohuan Zhao},
journal= {arXiv preprint arXiv:2103.05803},
year = {2025}
}
Comments
36 pages. Any suggestions and comments are welcome