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Stochastic Navier–Stokes equations with Caputo derivative driven by fractional noises
Guang-an Zou,
Guangying Lv,
Jiang-lun Wu 
Journal of Mathematical Analysis and Applications, Volume: 461, Issue: 1, Pages: 595 - 609
Swansea University Author:
Jiang-lun Wu
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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\"...
| Published in: | Journal of Mathematical Analysis and Applications |
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| ISBN: | ISSN: 0022-247X |
| ISSN: | 0022-247X |
| Published: |
Elsevier BV
2018
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| Online Access: |
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| URI: | https://cronfa.swan.ac.uk/Record/cronfa38087 |
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| 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\"{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. |
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| Keywords: |
Caputo derivative, stochastic Navier-Stokes equations, fractional Brownian motion, mild solutions. |
| College: |
Faculty of Science and Engineering |
| Issue: |
1 |
| Start Page: |
595 |
| End Page: |
609 |