In this paper, we are concerned with 3D tamed Navier-Stokes equations with periodic boundary conditions, which can be viewed as an approximation of the classical 3D Navier-Stokes equations. We show that the strong solution of 3D tamed Navier-Stokes equations driven by Poisson random measure converges weakly to the strong solution of 3D tamed Navier-Stokes equations driven by Gaussian noise on the state space $ \mathcal{D}([0, T];\mathbb{H}^1) $.
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