On the existence and long-time behavior of solutions to stochastic three-dimensional Navier–Stokes–Voigt equations

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ABSTRACTWe consider the 3D stochastic Navier–Stokes–Voigt equations in bounded domains with the homogeneous Dirichlet boundary condition and infinite-dimensional Wiener process. First, we prove the existence and uniqueness of solutions to the problem. Then we investigate the mean square exponential stability and the almost sure exponential stability of the stationary solutions.