Asymptotic autonomy of random attractors for non-autonomous stochastic Navier-Stokes equations on bounded domains

IF 1.3 4区 数学 Q1 MATHEMATICS
Kush Kinra, Renhai Wang, Manil T. Mohan
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引用次数: 2

Abstract

This article concerns the long-term random dynamics for a non-autonomous Navier-Stokes equation defined on a bounded smooth domain $ \mathcal{O} $ driven by multiplicative and additive noise. For the two kinds of noise driven equations, we demonstrate that the existence of a unique pullback attractor which is backward compact and asymptotically autonomous in $ \mathbb{L}^2(\mathcal{O}) $ and $ \mathbb{H}_0^1(\mathcal{O}) $, respectively. The compact embedding $ {\mathbb{H}}_0^1(\mathcal{O})\subset{\mathbb{L}}^2(\mathcal{O}) $ helps us to show the backward-uniform pullback asymptotic compactness (BUPAC) of the non-autonomous random dynamical systems (NRDS) in the Lebesgue space $ {\mathbb{L}}^2(\mathcal{O}) $. The backward-uniform flattening property of the solutions is used to prove the BUPAC of the NRDS in the Sobolev space $ \mathbb{H}_0^1(\mathcal{O}) $.
有界区域上非自治随机Navier-Stokes方程随机吸引子的渐近自治
本文研究了由乘性和加性噪声驱动的非自治Navier-Stokes方程在有界光滑域$ \mathcal{O} $上的长期随机动力学。对于这两类噪声驱动方程,我们分别证明了$ \mathbb{L}^2(\mathcal{O}) $和$ \mathbb{H}_0^1(\mathcal{O}) $中存在一个向后紧致且渐近自治的唯一的回拉吸引子。紧嵌入$ {\mathbb{H}}_0^1(\mathcal{O})\子集{\mathbb{L}}^2(\mathcal{O}) $帮助我们展示了Lebesgue空间$ {\mathbb{L}}^2(\mathcal{O}) $中非自治随机动力系统(NRDS)的后向均匀拉回渐近紧性(BUPAC)。利用解的后向均匀平坦性证明了NRDS在Sobolev空间$ \mathbb{H}_0^1(\mathcal{O}) $中的BUPAC。
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
Evolution Equations and Control Theory MATHEMATICS, APPLIED-MATHEMATICS
CiteScore
3.10
自引率
6.70%
发文量
5
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
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