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October  2008, 20(4): 961-974. doi: 10.3934/dcds.2008.20.961

Lyapunov exponents and the dimension of the attractor for 2d shear-thinning incompressible flow

P. Kaplický 1, and  Dalibor Pražák 2,

1. 

Charles University, Faculty of Mathematics and Physics, Department of Mathematical Analysis, Sokolovská 83, 186 75 Prague 8
2. 

Charles University in Prague, Faculty of Mathematics and Physics, Dept. of Mathematical Analysis, Sokolovská 83, 186 75 Praha 8, Czech Republic

Received  December 2006 Revised  October 2007 Published  January 2008

The equations describing planar motion of a homogeneous, incompressible generalized Newtonian fluid are considered. The stress tensor is given constitutively as $\T=\nu(1+\mu|\Du|^2)^{\frac{p-2}2}\Du$, where $\Du$ is the symmetric part of the velocity gradient. The equations are complemented by periodic boundary conditions.
    For the solution semigroup the Lyapunov exponents are computed using a slightly generalized form of the Lieb-Thirring inequality and consequently the fractal dimension of the global attractor is estimated for all $p\in(4/3,2]$.
Keywords: global attractor, Lieb-Thirring inequality., Power-law fluids, Lyapunov exponents, fractal dimension, shear-thinning fluids.
Mathematics Subject Classification: Primary: 37L30; Secondary: 35K2.
Citation: P. Kaplický, Dalibor Pražák. Lyapunov exponents and the dimension of the attractor for 2d shear-thinning incompressible flow. Discrete and Continuous Dynamical Systems, 2008, 20 (4) : 961-974. doi: 10.3934/dcds.2008.20.961
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