Abstract
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.
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Communicated by Y. Giga.
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Liu, G. Pullback Asymptotic Behavior of Solutions for a 2D Non-autonomous Non-Newtonian Fluid. J. Math. Fluid Mech. 19, 623–643 (2017). https://doi.org/10.1007/s00021-016-0299-9
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DOI: https://doi.org/10.1007/s00021-016-0299-9
Keywords
- Non-Newtonian fluid
- compact pullback absorbing set
- semigroup method
- \(\epsilon \)-regularity method
- pullback attractor
- flattening property