Asymptotic analysis of the equations ofmotion for viscoelastic oldroyd fluid

Kun Wang; Yangping Lin; Yinnian He

doi:10.3934/dcds.2012.32.657

Article Contents

2012, Volume 32, Issue 2: 657-677. Doi: 10.3934/dcds.2012.32.657

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Asymptotic analysis of the equations of motion for viscoelastic oldroyd fluid

1.
College of Mathematics and Statistics, Chongqing University, Chongqing 401331
2.
Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong
3.
Faculty of Science, Xi'an Jiaotong University, Xi'an 710049

Received: October 2010

Revised: June 2011

Published: February 2012

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Abstract

In this paper, the asymptotic analysis of the two-dimensional viscoelastic Oldroyd flows is presented. With the physical constant $\rho/\delta$ approaches zero, where $\rho$ is the viscoelastic coefficient and $1/\delta$ the relaxation time, the viscoelastic Oldroyd fluid motion equations converge to the viscous model known as the famous Navier-Stokes equations. Both the continuous and discrete uniform-in-time asymptotic errors are provided. Finally, the theoretical predictions are confirmed by some numerical experiments.

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Mathematics Subject Classification: Primary: 35L70, 76D05, 76A10.

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