arXiv subjects
Publications and source records attributed to Moez Benhamed.
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.
In this paper, we study the sub-critical dissipative quasi-geostrophic equations $({\bf S}_α)$. We prove that there exists a unique local-in-time solution for any large initial data $θ_0$ in the space ${\bf{\mathcal X}}^{1-2α}(\mathbb R^2)$ defined by (\ref{ec}). Moreover we show that $({\bf S}_α)$ has a global solution in time if the norms of the initial data in ${\bf{\mathcal X}}^{1-2α}(\mathbb R^2)$ are bounded by $1/4$. Also, we prove a blow-up criterion of the non global solution of $({\bf S}_α)$.