Stochastic Navier–Stokes equations with Caputo derivative driven by fractional noises - Jiang-lun Wu (Journal of Mathematical Analysis and Applications, 2018)
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 Hölder regularity of mild solutions to the given problem under certain sufficient conditions, which depend on the fractional order $α$ and Hurst parameter $H$. The results obtained in this study improve some results in existing literature.