Global attractors of two layer baroclinic quasi-geostrophic model

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