Random attractor associated with the quasi-geostrophic equation

2013/03/24 by Rongchan Zhu, Zhu, RongChan, Xiangchan Zhu +1 · 1 citation
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Probability (math.PR) #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.1303.5970

openalex publication_date 2013/03/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the long time behavior of the solutions to the 2D stochastic quasi-geostrophic equation on \mathbbT² 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.

Citations

• Random dynamical systems

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• Martingale solutions for stochastic active scalar equations perturbed by non-trace class noise

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