Journal
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
Volume 461, Issue 1, Pages 595-609Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jmaa.2018.01.027
Keywords
Caputo derivative; Stochastic Navier-Stokes equations; Fractional Brownian motion; Mild solutions
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Funding
- National Natural Science Foundation of China [11626085, 11771123]
- Postdoctoral Science Foundation of China [2016M600427, 2017T100385]
- Postdoctoral Science Foundation of Jiangsu Province, China [1601141B]
- Aid Project for the Leading Young Teachers in Henan Provincial Institutions of Higher Education of China [2015GGJS-024]
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In this paper, we consider the extended stochastic Navier-Stokes equations with Caputo derivative driven by fractional Brownian motion. We firstly derive the pathwise spatial and temporal regularity of the generalized Ornstein-Uhlenbeck process. Then we discuss the existence, uniqueness, and Holder regularity of mild solutions to the given problem under certain sufficient conditions, which depend on the fractional order a and Hurst parameter H. The results obtained in this study improve some results in existing literature. (C) 2018 Elsevier Inc. All rights reserved.
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