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

In \cite{JAMH1}, we prove the well posedness of the quasi-geostrophic equation $(QG)_α\;,1/2<α\leq 1$, 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 $\|θ\|_{{\mathcal X}^{1-2α}}$ decays to zero as time goes to infinity.

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