Asymptotic Behavior of Solutions to Equations Modelling Non-Newtonian Flows

Abstract:

      This paper is concerned with the system of equations that model incompressible non-Newtonian fluid motion with $p$-growth dissipative potential $1+\frac{2n}{n+2}\leq p<3$ in $R^n$ $(n=2,3)$. Using the improved Fourier splitting method, we prove that a weak solution decays in $L^2$ norm at the same rate as $(1+t)^{-n/4}$ as the time $t$ approaches infinity.