SDEs with critical time dependent drifts: strong solutions

• 成果类型: Article
• 署名作者: Roeckner, Michael; Zhao, Guohuan
• 署名单位: University of Bielefeld; Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-025-01390-9
• 发表日期: 2025
• 页码: 1071-1111
• 关键词: STOCHASTIC DIFFERENTIAL-EQUATIONS; Navier-Stokes equations; sobolev diffusion; pathwise uniqueness; explicit formulas; singular drift; WEAK SOLUTIONS; REGULARITY; FLOWS

摘要

This paper is a continuation of (R & ouml;ckner and Zhao, Bernoulli 29(1), 821 757-784 (2023)). Based on a compactness criterion for random fields in Wiener-Sobolev spaces, in this paper, we prove the 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.