The Large-time Behavior Of The Compressible Fluid In 1-D And The Stability Of The Of The Boundary Layer Of The Non-Newtonian Fluid

In this paper,we study the large-time behavior of solutions to the problem of free bound-ary for the non-isentropic Navier-Stokes equations with density-dependent viscosity in one-dimensional,as well as stability of boundary layer to an outflow problem for a compressible non-Newtonian fluid in the half space.·Investigating the large-time behavior of solutions to the problem of free boundary for the non-isentropic Navier-Stokes equations with density-dependent viscosity in onedimensional,（?）,We prove that the classical solution is asymptotically stables as time tends to infinity by using elementary energy methods.·Investigating the initial boundary value problem（IBVP）for the one-dimensional compressible non-Newtonian flow on the half line R₊:=（0,∞）,which reads in Eulerian coordinates:（?）,withα>2 given constant,whereρ（x,t）0 and u（x,t）stand for the mass density and the velocity of the fluid respectively.p（ρ）=aρ^γis the pressure,where a>0,μ₀>0 and the exponentγ>1 are fixed constants.The main concern is to analyze the phenomena that the compressible non-Newtonian fluid blows out through the boundary.it is proved that there is a boundary layer（i.e.,the stationary solution）to the outflow problem.Furthermore,the boundary layer is nonlinearly stable under a small initial perturbation.