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Discrete Dynamics in Nature and Society
Volume 2015 (2015), Article ID 627584, 13 pages
http://dx.doi.org/10.1155/2015/627584
Research Article

Approximation of a Class of Incompressible Third Grade Fluids Equations

1State Key Laboratory of Geomechanics and Geotechnical Engineering, Institute of Rock and Soil Mechanics, Chinese Academy of Sciences, Wuhan, Hubei 430071, China
2College of Science, Naval University of Engineering, Wuhan, Hubei 430033, China
3Power China Zhongnan Engineering Corporation Limited, Changsha, Hunan 410014, China

Received 21 October 2014; Revised 21 December 2014; Accepted 22 December 2014

Academic Editor: Ivan Area

Copyright © 2015 Zeqi Zhu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This paper discusses the approximation of weak solutions for a class of incompressible third grade fluids equations. We first introduce a family of perturbed slightly compressible third grade fluids equations (depending on a positive parameter ) which approximate the incompressible equations as . Then we prove the existence and uniqueness of weak solutions for the slightly compressible equations and establish that the solutions of the slightly compressible equations converge to the solutions of the incompressible equations.