On the uniqueness of the solution and finite-dimensional attractors for the 3D Flow with dynamic slip boundary condition

Abstract

We consider 3D incompressible non-Newtonian fluid, subject to a dynamic boundary condition. Using an iteration scheme in Nikolski-Bochner spaces, we obtain additional fractional time regularity of arbitrary weak solution, provided the power-law exponent is above the critical value $r = 11/5.$ This implies uniqueness of solutions. We also show existence of the global attractor and even a finite-dimensional exponential attractor.