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

Abstract

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 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.