Random Attractor Associated with the Quasi-Geostrophic Equation

Rong Chan Zhu; Xiang Chan Zhu

doi:10.1007/s10884-016-9537-3

Random Attractor Associated with the Quasi-Geostrophic Equation

Rong Chan Zhu, Xiang Chan Zhu^*

^*此作品的通讯作者

数学学院

科研成果: 期刊稿件 › 文章 › 同行评审

10 引用（Scopus）

摘要

We study the long time behavior of the solutions to the 2D stochastic quasi-geostrophic equation on T² driven by additive noise and real linear multiplicative noise in the subcritical case (i.e. α>12) by proving the existence of a random attractor. The key point for the proof is the exponential decay of the L^p-norm and a boot-strapping argument. The upper semicontinuity of random attractors is also established. Moreover, if the viscosity constant is large enough, the system has a trivial random attractor.

源语言	英语
页（从-至）	289-322
页数	34
期刊	Journal of Dynamics and Differential Equations
卷	29
期	1
DOI	https://doi.org/10.1007/s10884-016-9537-3
出版状态	已出版 - 1 3月 2017

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Zhu, R. C., & Zhu, X. C. (2017). Random Attractor Associated with the Quasi-Geostrophic Equation. Journal of Dynamics and Differential Equations, 29(1), 289-322. https://doi.org/10.1007/s10884-016-9537-3

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abstract = "We study the long time behavior of the solutions to the 2D stochastic quasi-geostrophic equation on T2 driven by additive noise and real linear multiplicative noise in the subcritical case (i.e. α>12) by proving the existence of a random attractor. The key point for the proof is the exponential decay of the Lp-norm and a boot-strapping argument. The upper semicontinuity of random attractors is also established. Moreover, if the viscosity constant is large enough, the system has a trivial random attractor.",

keywords = "Quasi-geostrophic equation, Random attractors, Random dynamical system, Stochastic flow, Stochastic partial differential equations",

author = "Zhu, {Rong Chan} and Zhu, {Xiang Chan}",

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N2 - We study the long time behavior of the solutions to the 2D stochastic quasi-geostrophic equation on T2 driven by additive noise and real linear multiplicative noise in the subcritical case (i.e. α>12) by proving the existence of a random attractor. The key point for the proof is the exponential decay of the Lp-norm and a boot-strapping argument. The upper semicontinuity of random attractors is also established. Moreover, if the viscosity constant is large enough, the system has a trivial random attractor.

AB - We study the long time behavior of the solutions to the 2D stochastic quasi-geostrophic equation on T2 driven by additive noise and real linear multiplicative noise in the subcritical case (i.e. α>12) by proving the existence of a random attractor. The key point for the proof is the exponential decay of the Lp-norm and a boot-strapping argument. The upper semicontinuity of random attractors is also established. Moreover, if the viscosity constant is large enough, the system has a trivial random attractor.

KW - Quasi-geostrophic equation

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Random Attractor Associated with the Quasi-Geostrophic Equation

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