SDEs with critical time dependent drifts: strong solutions

Fuente: arXiv

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Bibliographische Detailangaben
Hauptverfasser:	Röckner, Michael, Zhao, Guohuan
Format:	Preprint
Veröffentlicht:	2021
Schlagworte:	Probability
Online-Zugang:	Acceder al recurso
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author	Röckner, Michael Zhao, Guohuan
author_facet	Röckner, Michael Zhao, Guohuan
contents	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.
format	Preprint
id	arxiv_https___arxiv_org_abs_2103_05803
institution	arXiv
publishDate	2021
record_format	arxiv
spellingShingle	SDEs with critical time dependent drifts: strong solutions Röckner, Michael Zhao, Guohuan Probability 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.
title	SDEs with critical time dependent drifts: strong solutions
topic	Probability
url	https://arxiv.org/abs/2103.05803

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