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Abstract <p>The Voigt regularization of the Navier–Stokes system is studied in a bounded domain and on the torus. In the 3D case we obtain new explicit bounds for the attractor dimension improving the previously known results. In the 2D case we show that the estimates so obtained converge to the known estimates for the attractor of the Navier–Stokes system as the regularization parameter tends to zero both for the Dirichlet and the periodic boundary conditions.</p>

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Attractors for the Navier–Stokes–Voigt Equations and Their Dimension

  • 期刊论文

  • 发表日期：

    2025年9月1日

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  • A. A. Ilyin,
  • S. V. Zelik

摘要

Abstract

The Voigt regularization of the Navier–Stokes system is studied in a bounded domain and on the torus. In the 3D case we obtain new explicit bounds for the attractor dimension improving the previously known results. In the 2D case we show that the estimates so obtained converge to the known estimates for the attractor of the Navier–Stokes system as the regularization parameter tends to zero both for the Dirichlet and the periodic boundary conditions.