On the dimension of the attractor for a class of fluids with pressure dependent viscosities

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December 2005, 4(4): 805-822. doi: 10.3934/cpaa.2005.4.805

On the dimension of the attractor for a class of fluids with pressure dependent viscosities

M. Bulíček ^1, , Josef Málek ^2, and Dalibor Pražák ^3,

1.	Charles University, Faculty of Mathematics and Physics, Mathematical Institute, Sokolovská 83, 186 75 Prague 8, Czech Republic
2.	Mathematical Institute of the Charles University, Sokolovská 83, 186 73 Praha 8, Czech Republic
3.	Department of Mathematical Analysis, Charles University, Prague, Sokolovská 83, 186 75 Prague 8

Received November 2004 Revised April 2005 Published September 2005

Abstract
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We consider two-dimensional flows of an incompressible non Newtonian fluid where the departure from the Navier-Stokes fluid is due to the viscosity depending on both the rate of deformation and the pressure. We assume that the resulting extra-stress is uniformly elliptic and its derivative with respect to pressure is bounded in a proper manner. Considering just the spatially-periodic setting, one can prove the global existence and uniqueness of the strong solution. Using the so-called method of trajectories, we also prove the existence of an exponential attractor and estimate its fractal dimension in terms of the data of the equation.

Keywords: fractal dimension, exponential attractor, pressure-dependent viscosity, Non-newtonian fluid.

Mathematics Subject Classification: 76A05, 37L25, 37L30.

Citation: M. Bulíček, Josef Málek, Dalibor Pražák. On the dimension of the attractor for a class of fluids with pressure dependent viscosities. Communications on Pure & Applied Analysis, 2005, 4 (4) : 805-822. doi: 10.3934/cpaa.2005.4.805

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