Geodesic
Existence of global solutions to the 2-D subcritical dissipative quasi-geostrophic equation and persistency of the initial regularity
Electronic journal of differential equations, Tome 2011 (2011)
In this article, we prove that if the initial data

$ (\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 $C([0,+\infty [,X)$.
Classification : 35Q35, 76D03
Keywords: quasi-geostrophic equation, Besov spaces 
@article{EJDE_2011__2011__a50,
     author = {Ramzi,  May and Zahrouni,  Ezzeddine},
     title = {Existence of global solutions to the {2-D} subcritical dissipative quasi-geostrophic equation and persistency of the initial regularity},
     journal = {Electronic journal of differential equations},
     year = {2011},
     volume = {2011},
     zbl = {1220.35133},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2011__2011__a50/}
}
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%A Zahrouni,  Ezzeddine
%T Existence of global solutions to the 2-D subcritical dissipative quasi-geostrophic equation and persistency of the initial regularity
%J Electronic journal of differential equations
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%V 2011
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%F EJDE_2011__2011__a50
Ramzi,  May; Zahrouni,  Ezzeddine. Existence of global solutions to the 2-D subcritical dissipative quasi-geostrophic equation and persistency of the initial regularity. Electronic journal of differential equations, Tome 2011 (2011). http://geodesic.mathdoc.fr/item/EJDE_2011__2011__a50/