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

摘要

In this paper, we consider the extended stochastic Navier-Stokes equationswith Caputo derivative driven by fractional Brownian motion. We firstly derivethe pathwise spatial and temporal regularity of the generalizedOrnstein-Uhlenbeck process. Then we discuss the existence, uniqueness, andH\"{o}lder regularity of mild solutions to the given problem under certainsufficient conditions, which depend on the fractional order $\alpha$ and Hurstparameter $H$. The results obtained in this study improve some results inexisting literature.