  In \cite{JAMH1}, we prove the well posedness of the quasi-geostrophic
equation $(QG)_{\alpha}\;,1/2<\alpha\leq 1$, in the space introduced by Z. Lei
and F. Lin in \cite{ZY1}. In this chapter we discuss the long time behaviour.
Mainly, we prove that $\|\theta\|_{{\mathcal X}^{1-2\alpha}}$ decays to zero as
time goes to infinity.
