Existence and regularity of pullback attractors for a non-Newtonian fluid with delays in 2D unbounded domains

IF 1.3 4区数学 Q1 MATHEMATICS

Evolution Equations and Control Theory Pub Date : 2023-01-01 DOI:10.3934/eect.2023050

Guowei Liu, Hao Xu, Caidi Zhao

引用次数: 0

Abstract

This paper studies a non-autonomous incompressible non-Newtonian fluid with delay in a 2D unbounded domain. The existence of pullback $ \mathcal{D} $ attractor with $ \mathbb{H}^2 $ regularity is obtained and its relationship with the pullback $ \mathcal{D} $ attractor with $ \mathbb{L}^2 $ regularity obtained in [25] is also shown. This fact exhibits the pullback smoothing effect of the fluid with delays.

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二维无界区域上具有时滞的非牛顿流体的拉回吸引子的存在性和规律性

研究了二维无界区域上非自治不可压缩非牛顿流体的时滞问题。得到了具有$ \mathbb{H}^2 $正则性的回拉$ \mathcal{D} $吸引子的存在性，并给出了它与文献[25]中得到的具有$ \mathbb{L}^2 $正则性的回拉$ \mathcal{D} $吸引子的关系。这一事实显示了具有延迟的流体的回拉平滑效应。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Evolution Equations and Control Theory MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

3.10

自引率

6.70%

发文量

期刊介绍： EECT is primarily devoted to papers on analysis and control of infinite dimensional systems with emphasis on applications to PDE''s and FDEs. Topics include: * Modeling of physical systems as infinite-dimensional processes * Direct problems such as existence, regularity and well-posedness * Stability, long-time behavior and associated dynamical attractors * Indirect problems such as exact controllability, reachability theory and inverse problems * Optimization - including shape optimization - optimal control, game theory and calculus of variations * Well-posedness, stability and control of coupled systems with an interface. Free boundary problems and problems with moving interface(s) * Applications of the theory to physics, chemistry, engineering, economics, medicine and biology