A rate of convergence for the $\mathsf{LANS}\alpha$ regularization of Navier–Stokes equations

Abstract

A rate of convergence of the solutions of the $\mathsf{LANS}\alpha$ equations with periodic boundary to the solutions of the Navier–Stokes equations as $\alpha \downarrow 0$ is obtained in a mixed $L^1\text{–}{L}^2$ time–space norm for small initial data in Besov-type function spaces in which global existence and uniqueness of solutions can also be established.