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Well-Posedness for Stochastic Fractional Navier–Stokes Equation in the Critical Fourier–Besov Space

Xiuwei Yin, Jiang-lun Wu Orcid Logo, Guangjun Shen

Journal of Theoretical Probability, Volume: 35, Issue: 4

Swansea University Author: Jiang-lun Wu Orcid Logo

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DOI (Published version): 10.1007/s10959-021-01152-y

Abstract

This paper concerns the three-dimensional multiplicative stochastic fractional Navier-Stokesequation. Using Fourier localization technique, we establish the local existence and uniqueness of the solutions in the critical Fourier-Besov space $\mathcal{\dot{B}}^{4-2\alpha-\frac{3}{p}}_{p,r}$. Moreover...

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Published in: Journal of Theoretical Probability
ISSN: 0894-9840 1572-9230
Published: Springer Science and Business Media LLC 2022
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URI: https://cronfa.swan.ac.uk/Record/cronfa58983
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first_indexed 2021-12-09T12:49:23Z
last_indexed 2023-01-11T14:39:56Z
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spelling 2023-01-05T13:54:46.5334213 v2 58983 2021-12-09 Well-Posedness for Stochastic Fractional Navier–Stokes Equation in the Critical Fourier–Besov Space dbd67e30d59b0f32592b15b5705af885 0000-0003-4568-7013 Jiang-lun Wu Jiang-lun Wu true false 2021-12-09 SMA This paper concerns the three-dimensional multiplicative stochastic fractional Navier-Stokesequation. Using Fourier localization technique, we establish the local existence and uniqueness of the solutions in the critical Fourier-Besov space $\mathcal{\dot{B}}^{4-2\alpha-\frac{3}{p}}_{p,r}$. Moreover, when the initial date is sufficiently small, we obtain the global existence of the solutions in probability. Journal Article Journal of Theoretical Probability 35 4 Springer Science and Business Media LLC 0894-9840 1572-9230 stochastic fractional Navier-Stokes equation; Fourier-Besov space; strong solution. 1 12 2022 2022-12-01 10.1007/s10959-021-01152-y COLLEGE NANME Mathematics COLLEGE CODE SMA Swansea University SU Library paid the OA fee (TA Institutional Deal) Natural Science Foundation of China (Nos.11901005 and 12071003) and the Natural Science Foundation of Anhui Province (No. 2008085QA20) 2023-01-05T13:54:46.5334213 2021-12-09T12:42:24.6899782 Faculty of Science and Engineering School of Mathematics and Computer Science - Mathematics Xiuwei Yin 1 Jiang-lun Wu 0000-0003-4568-7013 2 Guangjun Shen 3 58983__22316__79062d53998841cfa0b5fcb2d83fd083.pdf 58983.pdf 2022-02-07T16:24:37.3231543 Output 351349 application/pdf Version of Record true © The Author(s) 2022. This article is licensed under a Creative Commons Attribution 4.0 International License true eng http://creativecommons.org/licenses/by/4.0/
title Well-Posedness for Stochastic Fractional Navier–Stokes Equation in the Critical Fourier–Besov Space
spellingShingle Well-Posedness for Stochastic Fractional Navier–Stokes Equation in the Critical Fourier–Besov Space
Jiang-lun Wu
title_short Well-Posedness for Stochastic Fractional Navier–Stokes Equation in the Critical Fourier–Besov Space
title_full Well-Posedness for Stochastic Fractional Navier–Stokes Equation in the Critical Fourier–Besov Space
title_fullStr Well-Posedness for Stochastic Fractional Navier–Stokes Equation in the Critical Fourier–Besov Space
title_full_unstemmed Well-Posedness for Stochastic Fractional Navier–Stokes Equation in the Critical Fourier–Besov Space
title_sort Well-Posedness for Stochastic Fractional Navier–Stokes Equation in the Critical Fourier–Besov Space
author_id_str_mv dbd67e30d59b0f32592b15b5705af885
author_id_fullname_str_mv dbd67e30d59b0f32592b15b5705af885_***_Jiang-lun Wu
author Jiang-lun Wu
author2 Xiuwei Yin
Jiang-lun Wu
Guangjun Shen
format Journal article
container_title Journal of Theoretical Probability
container_volume 35
container_issue 4
publishDate 2022
institution Swansea University
issn 0894-9840
1572-9230
doi_str_mv 10.1007/s10959-021-01152-y
publisher Springer Science and Business Media LLC
college_str Faculty of Science and Engineering
hierarchytype
hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Mathematics and Computer Science - Mathematics{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Mathematics and Computer Science - Mathematics
document_store_str 1
active_str 0
description This paper concerns the three-dimensional multiplicative stochastic fractional Navier-Stokesequation. Using Fourier localization technique, we establish the local existence and uniqueness of the solutions in the critical Fourier-Besov space $\mathcal{\dot{B}}^{4-2\alpha-\frac{3}{p}}_{p,r}$. Moreover, when the initial date is sufficiently small, we obtain the global existence of the solutions in probability.
published_date 2022-12-01T04:15:56Z
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score 11.037253

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