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SDEs with critical time dependent drifts: strong solutions

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arxiv 2103.05803 v5 pith:XC55JJJK submitted 2021-03-10 math.PR

Michael Röckner , Guohuan Zhao This is my paper · ORCID
classification math.PR
keywords criterioncriticalequationsprovesolutionsspacesstochasticstrong
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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.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. OpenAlex reports about 14 citations worldwide. Full citation record

  1. A new maximal regularity for parabolic equations and an application

    math.PR 2024-11 conditional novelty 8.0 of 10

    Maximal regularity in new Lebesgue-Holder-Dini spaces yields unique stochastic flows of homeomorphisms for SDEs with drift at the critical Dini exponent.

  2. Non-uniqueness of (Stochastic) Lagrangian Trajectories for Euler Equations

    math.AP 2025-04 conditional novelty 7.0 of 10

    Weak solutions of the Euler and Navier-Stokes equations exist for which two different particle trajectories start from the same point, in sharp regularity ranges, both with and without Brownian noise.

  3. Strong solutions of SDE's with rough coefficients

    math.PR 2025-07 reject novelty 6.0 of 10

    A Brownian SDE with merely measurable, Markovian drift is claimed to have a unique strong solution and H-C regular solution map whenever its Girsanov density has a finite L^{1+ε} moment.

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