SDEs with critical time dependent drifts: strong solutions
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2021
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| Acceso en línea: | |
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| _version_ | 1866913871314288640 |
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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 |