Electron. J. Diff. Eqns., Vol. 2005(2005), No. 125, pp. 1-13.

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

Bo-Qing Dong

This article concerns systems of equations that model incompressible bipolar non-Newtonian fluid motion in the whole space $\mathbb{R}^n$. Using the improved Fourier splitting method, we prove that a weak solution decays in the $L^2$ norm at the same rate as $(1+t)^{-n/4}$ as the time $t$ approaches infinity. Also we obtain optimal $L^2$ error-estimates for Newtonian and Non-Newtonian flows.

Submitted March 28, 2005. Published November 7, 2005.
Math Subject Classifications: 35B40, 35Q35, 76A05.
Key Words: Decay; bipolar non-Newtonian fluids; Fourier splitting method.

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Bo-Qing Dong
School of Mathematical Sciences
Nankai University
Tianjin 300071, China
email: bqdong@mail.nankai.edu.cn

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