Stochastic 3D Navier-Stokes equations with nonlinear damping: martingale solution, strong solution and small time large deviation principles

Abstract

In this paper, by using classical Faedo-Galerkin approximation and compactness method, the existence of martingale solutions for the stochastic 3D Navier-Stokes equations with nonlinear damping is obtained. The existence and uniqueness of strong solution are proved for $\beta >3$ with any $\alpha >0$ and $\alpha \ge \frac{1}{2}$ as $\beta =3$. Meanwhile, a small time large deviation principle for the stochastic 3D Navier-Stokes equation with damping is proved for $\beta >3$ with any $\alpha >0$ and $\alpha \ge \frac{1}{2}$ as $\beta =3$.

31 pages

References in corpus (3)

• The large deviation approach to statistical mechanics
• Global L_2-solutions of stochastic Navier-Stokes equations
• Local and global well-posedness of SPDE with generalized coercivity conditions