SDEs with critical time dependent drifts: strong solutions

2021/03/10 by Röckner, Michael, Zhao, Guohuan · 2 citations
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2103.05803

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.

Cited by

• The Euler-Maruyama method for SDEs with low-regularity drift
• Strong solutions of SDE's with rough coefficients

Related

• SDEs with critical time dependent drifts: weak solutions
• Stochastic Differential Equations with Critical Drifts
• Strong solutions of SDE's with rough coefficients
• On weak solutions of stochastic differential equations with sharp drift coefficients
• SDEs with subcritical Lebesgue--Hölder drift and driven by α-stable processes