# American Institute of Mathematical Sciences

July  2019, 18(4): 2133-2161. doi: 10.3934/cpaa.2019096

## Large-time behavior of solution to an inflow problem on the half space for a class of compressible non-Newtonian fluids

 School of Mathematics and CNS, Northwest University, Xi'an 710069, China

* Corresponding author

Received  August 2018 Revised  October 2018 Published  January 2019

Fund Project: This work is supported by the NSFC grant 11331005, 11671319 and 11801444.

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.

Citation: Zhenhua Guo, Wenchao Dong, Jinjing Liu. Large-time behavior of solution to an inflow problem on the half space for a class of compressible non-Newtonian fluids. Communications on Pure & Applied Analysis, 2019, 18 (4) : 2133-2161. doi: 10.3934/cpaa.2019096
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