Random attractor associated with the quasi-geostrophic equation

RongChan Zhu; XiangChan Zhu

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arXiv · 1303.5970

Random attractor associated with the quasi-geostrophic equation

RongChan Zhu·XiangChan Zhu

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Abstract

We study the long time behavior of the solutions to the 2D stochastic quasi-geostrophic equation on $\mathbb{T}^2$ driven by additive noise and real linear multiplicative noise in the subcritical case (i.e. $α>1/2$) 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.

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RongChan Zhu, XiangChan Zhu. 2013-03-24. Random attractor associated with the quasi-geostrophic equation. https://arxiv.org/abs/1303.5970

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