Modeling Error of $\alpha$-Models of Turbulence on a Two-Dimensional Torus
Résumé
This paper is devoted to study the rate of convergence of the weak solutions $u_\alpha$ of $\alpha$-regularization models to the weak solution $bu$ of the Navier-Stokes equations in the two-dimensional periodic case, as the regularization parameter $\alpha$ goes to zero. More specifically, we will consider the Leray-$\alpha$, the simplified Bardina, and the modified Leray-$\alpha$ models. Our aim is to improve known results in terms of convergence rates and also to show estimates valid over long time intervals.
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