Finite fractal dimension of the global attractor for a class of non-Newtonian fluids Original Research Article

We present a new criterion of finiteness of the fractal dimension of the attractor via the method of short trajectories developed in [1]. As an application, we deal with the so-called generalized Navier-Stokes equations characterized by nonlinear polynomial dependence of (p − 1) order between the stress tensor and the symmetric velocity gradient. We study the case p ≥ 2 subject to space-periodic boundary conditions. The existence of the global attractor with finite fractal dimension is then obtained in the following cases: 1. (i) in two dimensions if p ≥ 2, and 2. (ii) in three dimensions if View the MathML source.