Theorems about the attractor for incompressible non-Newtonian flow driven by external forces that are rapidly oscillating in time but have a smooth average |
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Authors: | Caidi Zhao Shengfan Zhou Yongsheng Li |
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Institution: | aSchool of Mathematics and Information Science, Wenzhou University, Zhejiang 325035, PR China;bDepartment of Applied Mathematics, Shanghai Normal University, Shanghai 200444, PR China;cDepartment of Applied Mathematics, South China University of Technology, Guangdong 510640, PR China |
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Abstract: | This paper discusses the incompressible non-Newtonian fluid with rapidly oscillating external forces g (x,t)=g(x,t,t/ ) possessing the average g0(x,t) as →0+, where 0<![var epsilon var epsilon](http://www.sciencedirect.com/scidirimg/entities/25b.gif) ![less-than-or-equals, slant less-than-or-equals, slant](http://www.sciencedirect.com/scidirimg/entities/2a7d.gif) 0<1. Firstly, with assumptions (A1)–(A5) on the functions g(x,t,ξ) and g0(x,t), we prove that the Hausdorff distance between the uniform attractors and in space H, corresponding to the oscillating equations and the averaged equation, respectively, is less than O( ) as →0+. Then we establish that the Hausdorff distance between the uniform attractors and in space V is also less than O( ) as →0+. Finally, we show for each ![var epsilon var epsilon](http://www.sciencedirect.com/scidirimg/entities/25b.gif) 0, 0]. |
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Keywords: | Incompressible non-Newtonian fluid Uniform attractor Oscillating external forces Time averaging |
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