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

The equations describing planar motion of a homogeneous, incompressible generalized Newtonian fluid are considered. The stress tensor is given constitutively as Gamma - nu(1 +mu |Du|(2))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 is an element of (4/3, 2].