On the dimension of the attractor for a class of fluids with pressure dependent viscosities
The authors consider two-dimensional flows of an incompressible non-Newtonian fluid where the difference from the Navier-Stokes fluid is due to the viscosity depending on both the rate of deformation and the pressure. They prove the global existence and uniqueness of weak solutions. The authors establish the so-called ``smoothing property'' of the equation in the space of trajectories. Based on the last ``smoothing property'' they prove the existence of an exponential attractor and estimate its fractal dimension in terms of the data of the equation.
scientific article; zbMATH DE number 5000544