Global attractors of two layer baroclinic quasi-geostrophic model

Yanhong Zhang

doi:10.3934/dcdsb.2021023

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2021, Volume 26, Issue 12: 6377-6385. Doi: 10.3934/dcdsb.2021023 open access

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Global attractors of two layer baroclinic quasi-geostrophic model

Yanhong Zhang

School of Mathematics, Lanzou City University, Lanzhou, 730070, China

Received: July 2020

Early access: January 2021

Published: December 2021

The work was supported in part by the National Science Foundation of China under Grant 11761044.

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Abstract

We study the dynamics of a two-layer baroclinic quasi-geostrophic model. We prove that the semigroup $ \{S(t)\}_{t\geq 0} $ associated with the solutions of the model has a global attractor in both $ {{\dot H}_{p}}^1(\Omega) $ and $ {{\dot H}_{p}}^2(\Omega) $. Also we show that for any viscosity $ \mu>0 $, there is an open and dense set of forcing $ \mathcal G\subset{{\dot H}_{p}}^0(\Omega) $ such that for each $ G = (g_1, g_2)\in \mathcal G $, the set $ S(G, \mu) \subset {{\dot H}_{p}}^4(\Omega) $ of the steady state problem is non–empty and finite.

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Mathematics Subject Classification: 37C70.

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References

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