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

Abstract

Regularization of the Navier-Stokes equations by adding hyperviscosity term $\mu(-\Delta^{2})$, $\mu \gt 0$ 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.