Global regularity for a modified critical dissipative quasi-geostrophic equation

Details Global regularity for a modified critical dissipative quasi-geostrophic equation Global regularity for a modified critical dissipative quasi-geostrophic equation

2008-03-09

arxiv.org/abs/0803.1318v1

Indiana Univ. Math. J. 57 (2008), no. 6, 2681--2692

Mathematics

Analysis of PDEs

9 pages

Scientific paper

10.1512/iumj.2008.57.3629

In this paper, we consider the modified quasi-geostrophic equation \begin{gather*} \del_t \theta + (u \cdot \grad) \theta + \kappa \Lambda^\alpha \theta = 0 u = \Lambda^{\alpha - 1} R^{\perp}\theta. \end{gather*} with $\kappa > 0$, $\alpha \in (0,1]$ and $\theta_0 \in \lp{2}(\R^2)$. We remark that the extra $\Lambda^{\alpha - 1}$ is introduced in order to make the scaling invariance of this system similar to the scaling invariance of the critical quasi-geostrophic equations. In this paper, we use Besov space techniques to prove global existence and regularity of strong solutions to this system.

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