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We obtain the existence, regularity, uniqueness of the non-stationaryproblems of a class of non-Newtonian fluid is a power law fluid with $p>9/5$ inthe half-space under slip boundary conditions.

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