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On Convergence of Galerkin's Approximations for the Regularized 3D Periodic Navier-Stokes Equations

Commun. Math. Anal.
Volume 14, Number 2 (2013), 103 - 112

On Convergence of Galerkin's Approximations for the Regularized 3D Periodic Navier-Stokes Equations

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Abstract

Regularization of the Navier-Stokes equations by adding hyperviscosity term μ(−Δ2), μ > 0 is considered. We proved convergence of Galerkin’s approximations to the strong generalized solution of the regularized Navier-Stokes equations; existence and uniqueness of the strong generalized solution.