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:???,with?>2 given constant,where??x,t?0 and u?x,t?stand for the mass density and the velocity of the fluid respectively.p???=a?^?is the pressure,where a>0,?₀>0 and the exponent?>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.