Existence, regularity and uniqueness of weak solutions for a class of incompressible generalized Navier-Stokes system with slip boundary conditions in ${\mathbb{R}}_{+}^3$

We obtain the existence, regularity, uniqueness of the non-stationary problems of a class of non-Newtonian fluid is a power law fluid with $p>9\mathrm{/}5$ in the half-space under slip boundary conditions.