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Stochastic Navier–Stokes equations with Caputo derivative driven by fractional noises

Guang-an Zou, Guangying Lv, Jiang-lun Wu Orcid Logo

Journal of Mathematical Analysis and Applications, Volume: 461, Issue: 1, Pages: 595 - 609

Swansea University Author: Jiang-lun Wu Orcid Logo

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DOI (Published version): 10.1016/j.jmaa.2018.01.027

Abstract

In this paper, we consider the extended stochastic Navier-Stokes equations with Caputo derivative driven by fractionalBrownian motion. We firstly derive the pathwise spatial and temporal regularity of the generalized Ornstein-Uhlenbeck process. Then we discuss the existence, uniqueness, and H\"...

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Published in: Journal of Mathematical Analysis and Applications
ISBN: ISSN: 0022-247X
ISSN: 0022-247X
Published: Elsevier BV 2018
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URI: https://cronfa.swan.ac.uk/Record/cronfa38087
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first_indexed 2018-01-14T20:15:41Z
last_indexed 2020-07-28T12:57:25Z
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spelling 2020-07-28T11:19:50.0404527 v2 38087 2018-01-14 Stochastic Navier–Stokes equations with Caputo derivative driven by fractional noises dbd67e30d59b0f32592b15b5705af885 0000-0003-4568-7013 Jiang-lun Wu Jiang-lun Wu true false 2018-01-14 SMA In this paper, we consider the extended stochastic Navier-Stokes equations with Caputo derivative driven by fractionalBrownian motion. We firstly derive the pathwise spatial and temporal regularity of the generalized Ornstein-Uhlenbeck process. Then we discuss the existence, uniqueness, and H\"{o}lder regularity of mild solutions to the given problem under certain sufficient conditions, which depend on the fractional order $\alpha$ and Hurst parameter $H$. The results obtained in this study improve some results in existing literature. Journal Article Journal of Mathematical Analysis and Applications 461 1 595 609 Elsevier BV ISSN: 0022-247X 0022-247X Caputo derivative, stochastic Navier-Stokes equations, fractional Brownian motion, mild solutions. 1 5 2018 2018-05-01 10.1016/j.jmaa.2018.01.027 COLLEGE NANME Mathematics COLLEGE CODE SMA Swansea University 2020-07-28T11:19:50.0404527 2018-01-14T15:48:35.4564084 Faculty of Science and Engineering School of Mathematics and Computer Science - Mathematics Guang-an Zou 1 Guangying Lv 2 Jiang-lun Wu 0000-0003-4568-7013 3 0038087-14012018155115.pdf TFSNSE-R1.pdf 2018-01-14T15:51:15.0930000 Output 264078 application/pdf Accepted Manuscript true 2019-05-01T00:00:00.0000000 true eng
title Stochastic Navier–Stokes equations with Caputo derivative driven by fractional noises
spellingShingle Stochastic Navier–Stokes equations with Caputo derivative driven by fractional noises
Jiang-lun Wu
title_short Stochastic Navier–Stokes equations with Caputo derivative driven by fractional noises
title_full Stochastic Navier–Stokes equations with Caputo derivative driven by fractional noises
title_fullStr Stochastic Navier–Stokes equations with Caputo derivative driven by fractional noises
title_full_unstemmed Stochastic Navier–Stokes equations with Caputo derivative driven by fractional noises
title_sort Stochastic Navier–Stokes equations with Caputo derivative driven by fractional noises
author_id_str_mv dbd67e30d59b0f32592b15b5705af885
author_id_fullname_str_mv dbd67e30d59b0f32592b15b5705af885_***_Jiang-lun Wu
author Jiang-lun Wu
author2 Guang-an Zou
Guangying Lv
Jiang-lun Wu
format Journal article
container_title Journal of Mathematical Analysis and Applications
container_volume 461
container_issue 1
container_start_page 595
publishDate 2018
institution Swansea University
isbn ISSN: 0022-247X
issn 0022-247X
doi_str_mv 10.1016/j.jmaa.2018.01.027
publisher Elsevier BV
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 In this paper, we consider the extended stochastic Navier-Stokes equations with Caputo derivative driven by fractionalBrownian motion. We firstly derive the pathwise spatial and temporal regularity of the generalized Ornstein-Uhlenbeck process. Then we discuss the existence, uniqueness, and H\"{o}lder regularity of mild solutions to the given problem under certain sufficient conditions, which depend on the fractional order $\alpha$ and Hurst parameter $H$. The results obtained in this study improve some results in existing literature.
published_date 2018-05-01T03:48:08Z
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score 11.037144

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