Existence of weak solutions for non-stationary flows of fluids with shear thinning dependent viscosities under slip boundary conditions in half space

This paper treats the system of motion for an incompressible non-Newtonian fluids of the stress tensor described by p-potential function subject to slip boundary conditions in ? ₊ ³ . Making use of the Oseentype approximation to this model and the L^∞-truncation method, one can establish the existence theorem of weak solutions for p-potential flow with p ∈ ((frac{8}{5}), 2] provided that large initial are regular enough.