Journal of Mathematical Fluid Mechanics

, Volume 19, Issue 4, pp 623–643 | Cite as

Pullback Asymptotic Behavior of Solutions for a 2D Non-autonomous Non-Newtonian Fluid

  • Guowei LiuEmail author


This paper studies the pullback asymptotic behavior of solutions for the non-autonomous incompressible non-Newtonian fluid in 2D bounded domains. Firstly, with a little high regularity of the force, the semigroup method and \(\epsilon \)-regularity method are used to establish the existence of compact pullback absorbing sets. Then, with a minimal regularity of the force, by verifying the flattening property also known as the “Condition (C)”, the author proves the existence of pullback attractors for the universe of fixed bounded sets and for the another universe given by a tempered condition. Furthermore, the regularity of pullback attractors is given.


Non-Newtonian fluid compact pullback absorbing set semigroup method \(\epsilon \)-regularity method pullback attractor flattening property 

Mathematics Subject Classification

Primary 35B41 Secondary 35Q35 76D03 


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Copyright information

© Springer International Publishing 2016

Authors and Affiliations

  1. 1.School of Mathematical SciencesShanghai Jiao Tong UniversityShanghaiPeople’s Republic of China

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