一类非牛顿流体模型解的渐近性态(英)

本文主要讨论一类带 $p \,\,( 1+\frac{2n}{n+2} \leq p<3 )\,$ 幂增长耗散位势的非牛顿流体模型解的渐近性态, 利用改进的 Fourier分解方法, 证明了其解在$L^2$ 范数下衰减率为 $(1+t)^{-\frac{n}{4}}$.

Asymptotic Behavior of Solutions to Equations Modelling Non-Newtonian Flows

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.