The Existence and Dimension of the Attractor for a 3D Flow of a Non-Newtonian Fluid subject to Dynamic Boundary Conditions

We consider non-Newtonian incompressible 3D fluid of Ladyzhenskaya type, in the setting of the dynamic boundary condition. Assuming sufficient growth rate of the stress tensor with respect to the velocity gradient, we establish explicit dimension estimate of the global attractor in terms of the physical parameters of the problem.