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^*

^*Corresponding author for this work

School of Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

10 Citations (Scopus)

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 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.

Original language	English
Pages (from-to)	289-322
Number of pages	34
Journal	Journal of Dynamics and Differential Equations
Volume	29
Issue number	1
DOIs	https://doi.org/10.1007/s10884-016-9537-3
Publication status	Published - 1 Mar 2017

Keywords

Quasi-geostrophic equation
Random attractors
Random dynamical system
Stochastic flow
Stochastic partial differential equations

Access to Document

10.1007/s10884-016-9537-3

Cite this

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

@article{f1231bd9320849399dc7f19e51234d78,

title = "Random Attractor Associated with the Quasi-Geostrophic Equation",

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}",

note = "Publisher Copyright: {\textcopyright} 2016, Springer Science+Business Media New York.",

year = "2017",

month = mar,

day = "1",

doi = "10.1007/s10884-016-9537-3",

language = "English",

volume = "29",

pages = "289--322",

journal = "Journal of Dynamics and Differential Equations",

issn = "1040-7294",

publisher = "Springer New York",

number = "1",

}

TY - JOUR

T1 - Random Attractor Associated with the Quasi-Geostrophic Equation

AU - Zhu, Rong Chan

AU - Zhu, Xiang Chan

PY - 2017/3/1

Y1 - 2017/3/1

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

KW - Random attractors

KW - Random dynamical system

KW - Stochastic flow

KW - Stochastic partial differential equations

UR - http://www.scopus.com/inward/record.url?scp=84969945307&partnerID=8YFLogxK

U2 - 10.1007/s10884-016-9537-3

DO - 10.1007/s10884-016-9537-3

M3 - Article

AN - SCOPUS:84969945307

SN - 1040-7294

VL - 29

SP - 289

EP - 322

JO - Journal of Dynamics and Differential Equations

JF - Journal of Dynamics and Differential Equations

IS - 1

ER -

Random Attractor Associated with the Quasi-Geostrophic Equation

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this