Theorems about the attractor for incompressible non-Newtonian flow driven by external forces that are rapidly oscillating in time but have a smooth average
✍ Scribed by Caidi Zhao; Shengfan Zhou; Yongsheng Li
- Publisher
- Elsevier Science
- Year
- 2008
- Tongue
- English
- Weight
- 227 KB
- Volume
- 220
- Category
- Article
- ISSN
- 0377-0427
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✦ Synopsis
This paper discusses the incompressible non-Newtonian fluid with rapidly oscillating external forces g ε (x, t) = g(x, t, t/ε) possessing the average g 0 (x, t) as ε → 0 + , where 0 < ε ε 0 < 1. Firstly, with assumptions (A 1 )-(A 5 ) on the functions g(x, t, ) and g 0 (x, t), we prove that the Hausdorff distance between the uniform attractors A ε and A 0 in space H, corresponding to the oscillating equations and the averaged equation, respectively, is less than O(ε) as ε → 0 + . Then we establish that the Hausdorff distance between the uniform attractors A V ε and A V 0 in space V is also less than O(ε) as ε → 0 + . Finally, we show A ε ⊆ A V ε for each ε ∈ [0, ε 0 ].