article

Title: Global regularity for a modified critical dissipative quasi-geostrophic equation

Authors: Peter Constantin, Gautum Iyer and Jiahong Wu

Issue: Volume 57 (2008), Issue 6, 2681-2692

Abstract:

$In this paper, we consider the modified quasi-geostrophic equation \begin{gather*} \partial_{t} \theta + (u \cdot \nabla) \theta + \kappa \Lambda^{\alpha} \theta = 0\\ u = \Lambda^{\alpha - 1} R^{\perp}\theta, \end{gather*} with $\kappa > 0$, $\alpha \in (0,1]$ and $\theta_0 \in L^{2}(\mathbb{R}^2)$. 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.$