Decay of solutions to equations modelling incompressible bipolar non-newtonian fluids

Abstract

This article concerns systems of equations that model incompressible bipolar non-Newtonian fluid motion in the whole space ℝn. Using the improved Fourier splitting method, we prove that a weak solution decays in the L2 norm at the same rate as (1 + t)-n/4 as the time t approaches infinity. Also we obtain optimal L2 error-estimates for Newtonian and Non-Newtonian flows.