https://www.research.manchester.ac.uk/portal/files/46813289/MDP_NS_jump.pdf

A moderate deviation principle for 2-D stochastic Navier–Stokes equations driven by multiplicative Lévy noises ☆

In this paper, we establish a moderate deviation principle for two-dimensional stochastic Navier-Stokes equations driven by multiplicative $L\acute{e}vy$ noises. The weak convergence method introduced by Budhiraja, Dupuis and Ganguly in arXiv:1401.73v1 plays a key role.

A Moderate Deviation Principle for 2-D Stochastic Navier-Stokes Equations Driven by Multiplicative L\'evy Noises

https://cronfa.swan.ac.uk/Record/cronfa38087/Download/0038087-14012018155115.pdf

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

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 Holder regularity of mild solutions to the given problem under certain sufficient conditions, which depend on the fractional order $\alpha$ and Hurst parameter $H$. The results obtained in this study improve some results in existing literature.

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

In this paper, we establish a large deviation principle for stochastic models of incompressible second grade fluids. The weak convergence method introduced by Budhiraja and Dupuis (Probab Math Statist 20:39–61, 2000) plays an important role.

Large Deviations for Stochastic Models of Two-Dimensional Second Grade Fluids

http://staff.ustc.edu.cn/~wangran/Papers/MDP-NS.pdf

Jian Liang Zhai

Papers

A moderate deviation principle for 2-D stochastic Navier-Stokes equations