Abstract
In this paper, we study the large time behaviors of boundary layer solution of the inflow problem on the half space for a class of isentropic compressible non-Newtonian fluids. We establish the existence and uniqueness of the boundary layer solution to the non-Newtonian fluids. Especially, it is shown that such a boundary layer solution have a maximal interval of existence. Then we prove that if the strength of the boundary layer solution and the initial perturbation are suitably small, the unique global solution in time to the non-Newtonian fluids exists and asymptotically tends toward the boundary layer solution. The proof is given by the elementary energy method.
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