Limit stationary statistical solutions of stochastic Navier-Stokes-Voigt equation in a 3D thin domain

This work is concerned with limit behavior of the Navier-Stokes-Voigt equation with degenerate white noise in a 3D thin domain. Although the individual solutions may be chaotic in fluid dynamics, the stationary statistical solutions are essential to capture complex dynamical behaviors in the view of statistic. We therefore prove that the stationary statistical solution of the system converges weakly to the counterpart of the 2D stochastic Euler equation as the viscosity, the elasticity parameter and the thickness of the thin domain tend to zero.