# American Institute of Mathematical Sciences

February  2012, 32(2): 657-677. doi: 10.3934/dcds.2012.32.657

## Asymptotic analysis of the equations of motion for viscoelastic oldroyd fluid

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

Received  October 2010 Revised  June 2011 Published  September 2011

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.
Citation: Kun Wang, Yangping Lin, Yinnian He. Asymptotic analysis of the equations of motion for viscoelastic oldroyd fluid. Discrete & Continuous Dynamical Systems - A, 2012, 32 (2) : 657-677. doi: 10.3934/dcds.2012.32.657
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##### References:
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