Stochastic 3D Leray-$α$ Model with Fractional Dissipation
Shihu Li,
Wei Liu,
Yingchao Xie
Abstract:In this paper, we establish the global well-posedness of stochastic 3D Leray-α model with general fractional dissipation driven by multiplicative noise. This model is the stochastic 3D Navier-Stokes equations regularized through a smoothing kernel of order θ 1 in the nonlinear term and a θ 2 -fractional Laplacian. In the case of θ 1 ≥ 0 and θ 2 > 0 with θ 1 + θ 2 ≥ 5 4 , we prove the global existence and uniqueness of the strong solutions. The main results cover many existing works in the deterministic cases, … Show more
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