American Institute of Mathematical Sciences

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

 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

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.
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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