Global attractors of two layer baroclinic quasi-geostrophic model

Abstract

<p style='text-indent:20px;'>We study the dynamics of a two-layer baroclinic quasi-geostrophic model. We prove that the semigroup <inline-formula><tex-math id="M1">\begin{document}$ \{S(t)\}_{t\geq 0} $\end{document}</tex-math></inline-formula> associated with the solutions of the model has a global attractor in both <inline-formula><tex-math id="M2">\begin{document}$ {{\dot H}_{p}}^1(\Omega) $\end{document}</tex-math></inline-formula> and <inline-formula><tex-math id="M3">\begin{document}$ {{\dot H}_{p}}^2(\Omega) $\end{document}</tex-math></inline-formula>. Also we show that for any viscosity <inline-formula><tex-math id="M4">\begin{document}$ \mu&gt;0 $\end{document}</tex-math></inline-formula>, there is an open and dense set of forcing <inline-formula><tex-math id="M5">\begin{document}$ \mathcal G\subset{{\dot H}_{p}}^0(\Omega) $\end{document}</tex-math></inline-formula> such that for each <inline-formula><tex-math id="M6">\begin{document}$ G = (g_1, g_2)\in \mathcal G $\end{document}</tex-math></inline-formula>, the set <inline-formula><tex-math id="M7">\begin{document}$ S(G, \mu) \subset {{\dot H}_{p}}^4(\Omega) $\end{document}</tex-math></inline-formula> of the steady state problem is non–empty and finite.</p>