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Journal Articles Discrete and Continuous Dynamical Systems - Series B Year : 2021

Modeling Error of $\alpha$-Models of Turbulence on a Two-Dimensional Torus

Abstract

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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Dates and versions

hal-02469048 , version 1 (06-02-2020)
hal-02469048 , version 2 (12-02-2020)
hal-02469048 , version 3 (09-03-2020)

Identifiers

Cite

Luigi C. Berselli, Argus Adrian Dunca, Roger Lewandowski, Dinh Duong Nguyen. Modeling Error of $\alpha$-Models of Turbulence on a Two-Dimensional Torus. Discrete and Continuous Dynamical Systems - Series B, 2021, 26 (9), pp.4613-4643. ⟨10.3934/dcdsb.2020305⟩. ⟨hal-02469048v3⟩
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