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Global attractors of two layer baroclinic quasi-geostrophic model

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

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  • 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.

    Mathematics Subject Classification: 37C70.


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