Existence of global solutions to the 2-D subcritical dissipative quasi-geostrophic equation and persistency of the initial regularity
In this article, we prove that if the initial data $heta_0$ and its Riesz transforms ($mathcal{R}_1(heta_0)$ and $mathcal{R}_2(heta_0)$) belong to the space $$ (overline{S(mathbb{R}^2))} ^{B_{infty }^{1-2alpha ,infty }}, quad 1/2<alpha <1, $$ then the 2-D Quasi-Geostrophic equa...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Texas State University
2011-01-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2011/08/abstr.html |
| Summary: | In this article, we prove that if the initial data $heta_0$ and its Riesz transforms ($mathcal{R}_1(heta_0)$ and $mathcal{R}_2(heta_0)$) belong to the space $$ (overline{S(mathbb{R}^2))} ^{B_{infty }^{1-2alpha ,infty }}, quad 1/2<alpha <1, $$ then the 2-D Quasi-Geostrophic equation with dissipation $alpha$ has a unique global in time solution $heta$. Moreover, we show that if in addition $heta_0 in X$ for some functional space $X$ such as Lebesgue, Sobolev and Besov's spaces then the solution $heta$ belongs to the space $C([0,+infty [,X)$. |
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| ISSN: | 1072-6691 |