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arXiv · 0908.0199

Global Existence of Solutions to the 2D subcritical dissipative Quasi-Geostrophic equation and persistency of the initial regularity

Ramzi May·Ezzeddine Zahrouni
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Abstract

In this paper, we prove that if the initial data $θ_0$ and its Riesz transforms ($\mathcal{R}_1(θ_0)$ and $\mathcal{R}_2(θ_0)$) belong to the space $(\overline{S(\mathbb{R}^2))}^{B_{\infty}^{1-2α,\infty}}$, where $α\in ]1/2,1[$, then the 2D Quasi-Geostrophic equation with dissipation $α$ has a unique global in time solution $θ$. Moreover, we show that if in addition $θ_0 \in X$ for some functional space $X$ such as Lebesgue, Sobolev and Besov's spaces then the solution $θ$ belongs to the space $C([0,+\infty [,X).$

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Ramzi May, Ezzeddine Zahrouni. 2009-08-03. Global Existence of Solutions to the 2D subcritical dissipative Quasi-Geostrophic equation and persistency of the initial regularity. https://arxiv.org/abs/0908.0199

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