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.