Publication at Faculty of Mathematics and Physics |
2007
Abstract
We study the dynamics of an incompressible, homogeneous fluid of a power-law type, with the stress tensor $\TT=\nu(1+\mu |Dv|)^{p-2}Dv$, where $Dv$ is a symmetric velocity gradient. We consider the two-dimensional problem with periodic boundary conditions and $p\in(1,2)$.
Under these assumptions, we estimate the fractal dimension of the exponential attractor, using the so-called method of $\ell$-trajectories.