Stochastic 3D tamed Navier–Stokes equations: Existence, uniqueness and small time large deviation principles

In this paper, we first give a direct approach to the existence and uniqueness of strong solutions to stochastic 3D tamed Navier–Stokes equations in case of Dirichlet boundary conditions for the Stokes–Laplacian. Then we prove a small time large deviation principle for the solutions.