Martingale solutions and invariant measures for stochastic fractional Navier–Stokes equations on unbounded 3 dimension domains

This paper investigates the existence of martingale solution and invariant measure for the stochastic fractional Navier–Stokes equations on unbounded 3 dimension domains. By the Faedo–Galerkin approximation, a tightness criterion and the Skorokhod theorem, we get the existence of martingale solution for the equation. We also show that if the Lipschitz constant L of nonlinear function of random external force term is less than 2, then the martingale solution is the strong solution in the sense of probability. By this fact, using the weak Feller method, we get the existence of invariant measure for the equation.