Electronic Journal of Differential Equations,
Vol. 2011 (2011), No. 08, pp. 1-18.
Title: Existence of global solutions to the 2-D subcritical dissipative
quasi-geostrophic equation and persistency of the initial regularity
Authors: May Ramzi (Faculte des Sciences de Bizerte, Tunisie)
Ezzeddine Zahrouni (Faculte des Sciences de Monastir, Tunisie)
Abstract:
In this article, we prove that if the initial data $\theta_0$ and
its Riesz transforms ($\mathcal{R}_1(\theta_0)$ and
$\mathcal{R}_2(\theta_0)$) belong to the space
$$
(\overline{S(\mathbb{R}^2))} ^{B_{\infty }^{1-2\alpha ,\infty }},
\quad 1/2<\alpha <1,
$$
then the 2-D Quasi-Geostrophic
equation with dissipation $\alpha$ has a unique global in time
solution $\theta$. Moreover, we show that if in addition
$\theta_0 \in X$ for some functional space $X$ such as
Lebesgue, Sobolev and Besov's spaces then the solution $\theta$
belongs to the space $C([0,+\infty [,X)$.
Submitted August 10, 2010. Published January 15, 2011.
Math Subject Classifications: 35Q35, 76D03
Key Words: Quasi-geostrophic equation; Besov Spaces