Large Time Behaviour And Energy Decay Estimation Of A Class Of Compressible Non-Newtonian Fluid Weak Solutions

In this paper,we study the large time behaviour of the weak solutions of a class of compressible non-Newtonian fluid in a bounded domain of three-dimensional spaces.And the decay estimates of energy of the equations is given when the external force is zero.First,the large time behaviour of weak solutions to the initial boundary value problem of compressible non-Newtonian fluid equations is studied#12?=??(?>3/2),T(Du)=|Du|p-2Du+v|div u|p-2 div u ?(v?0,p>1).In order to improve the regularity of fluid density?operator A is used to estimate pressure term to get the high-order integrability result of density.We prove that weak solutions of compressible non-Newtonian fluid equations converged to a fixed stationary state as time goes to infinity by using energy method.Next,we get the decay estimates of the energy of this model under the condition of external force is zero by constructing a Lyapunov function and assuming the fluid density has an upper bound.