SDEs with critical time dependent drifts: strong solutions

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.

36 pages. Any suggestions and comments are welcome

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Cited by in corpus (5)

• Global $L_p$ estimates for kinetic Kolmogorov-Fokker-Planck equations in nondivergence form
• SDEs with critical time dependent drifts: weak solutions
• Solution theory of fractional SDEs in complete subcritical regimes
• Existence of strong solutions for Itô's stochastic equations via approximations. Revisited
• On diffusion processes with drift in a Morrey class containing $L_{d+2}$