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

2017/09/15 by Zou, Guang-an, Lv, Guangying, Wu, Jiang-Lun
#FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.1709.05028

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.

Related

• Distribution-flow dependent SDEs driven by (fractional) Brownian motion and Navier-Stokes equations
• Strong solutions for singular SDEs driven by long-range dependent fractional Brownian motion and other Volterra processes
• Pathwise solutions to stochastic partial differential equations driven by fractional Brownian motions with Hurst parameters in (1/3,1/2]
• Existence and approximate controllability results for time-fractional stochastic Navier-Stokes equations
• On the fractional stochastic Navier-Stokes equations on the torus and on bounded domains