Decay-in-time of solutions for the compressible isentropic non-Newtonian fluids

Abstract

Motivated by the well-posedness result of non-Newtonian fluids in [Guo-Zhu, J. Differential Equations , 178 (2002), 281-297] and the large behavior result of Navier-Stokes system in [Li-Zhang, Math. Meth. Appl. Sci, 34 (2011), 670-682], we investigate the decay-in-time of solutions for a three-dimensional compressible non-Newtonian fluid. In this paper, we consider the large time behavior of solutions to the Cauchy problem for three-dimensional compressible isentropic non-Newtonian equations.