Long time decay to the solution to the 2D-DQG Equation

Abstract

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.