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Global Attractors and a Lubrication Problem

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Navier–Stokes Equations

Part of the book series: Advances in Mechanics and Mathematics ((AMMA))

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Abstract

We start this chapter from necessary background on the theory of fractal dimension. Next, we formulate and study a problem which models the two-dimensional boundary driven shear flow in lubrication theory. After the derivation of the energy dissipation rate estimate and a version of Lieb–Thirring inequality we provide an estimate from above on the global attractor fractal dimension.

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Authors and Affiliations

  1. Faculty of Mathematics, Informatics, and Mechanics, University of Warsaw, Warszawa, Poland

    Grzegorz Łukaszewicz

  2. Faculty of Mathematics and Computer Science, Jagiellonian University in Krakow, Krakow, Poland

    Piotr Kalita

Authors
  1. Grzegorz Łukaszewicz
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  2. Piotr Kalita
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Łukaszewicz, G., Kalita, P. (2016). Global Attractors and a Lubrication Problem. In: Navier–Stokes Equations. Advances in Mechanics and Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-319-27760-8_9

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