Random Attractor Associated with the Quasi-Geostrophic Equation

被引：9
|
作者：
Zhu, RongChan [1 ,3 ]
Zhu, XiangChan [2 ,3 ]
机构：
[1] Beijing Inst Technol, Dept Math, Beijing 100081, Peoples R China
[2] Beijing Jiaotong Univ, Sch Sci, Beijing 100044, Peoples R China
[3] Univ Bielefeld, Dept Math, D-33615 Bielefeld, Germany
来源：
JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS | 2017年 / 29卷 / 01期
关键词：
Random attractors; Quasi-geostrophic equation; Random dynamical system; Stochastic flow; Stochastic partial differential equations; STOKES EQUATIONS;
D O I：
10.1007/s10884-016-9537-3
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We study the long time behavior of the solutions to the 2D stochastic quasi-geostrophic equation on driven by additive noise and real linear multiplicative noise in the subcritical case (i.e. ) by proving the existence of a random attractor. The key point for the proof is the exponential decay of the -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.
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页码：289 / 322
页数：34
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