Geodesic
Lieb--Thirring Integral Inequalities and Sharp Bounds for the Dimension of the Attractor of the Navier--Stokes Equations with Friction
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Function spaces, approximation theory, and nonlinear analysis, Tome 255 (2006), pp. 146-160.

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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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A. A. Ilyin. Lieb--Thirring Integral Inequalities and Sharp Bounds for the Dimension of the Attractor of the Navier--Stokes Equations with Friction. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Function spaces, approximation theory, and nonlinear analysis, Tome 255 (2006), pp. 146-160. http://geodesic.mathdoc.fr/item/TM_2006_255_a10/

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