Geodesic
Lieb–Thirring Integral Inequalities and Sharp Bounds for the Dimension of the Attractor of the Navier–Stokes Equations with Friction
Informatics and Automation, Function spaces, approximation theory, and nonlinear analysis, Tome 255 (2006), pp. 146-160 
A. A. Ilyin. Lieb–Thirring Integral Inequalities and Sharp Bounds for the Dimension of the Attractor of the Navier–Stokes Equations with Friction. Informatics and Automation, Function spaces, approximation theory, and nonlinear analysis, Tome 255 (2006), pp. 146-160. http://geodesic.mathdoc.fr/item/TRSPY_2006_255_a10/
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Voir la notice de l'article provenant de la source Math-Net.Ru

A two-dimensional Navier–Stokes system with friction is considered in a large rectangular periodic domain with area on the order of $\alpha^{-1}$, $\alpha \to 0$. Bounds for the dimension of the attractor are obtained, which are sharp both as $\alpha\to 0$ and $\nu\to 0$, where $\nu$ is the viscosity coefficient.

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