%0 Journal Article
%T Level Set Dynamics and the Non-blowup of the 2D Quasi-geostrophic Equation
%A Jian Deng
%A Thomas Y. Hou
%A Ruo Li
%A Xinwei Yu
%J Mathematics
%D 2006
%I arXiv
%X In this article we apply the technique proposed in Deng-Hou-Yu (Comm. PDE, 2005) to study the level set dynamics of the 2D quasi-geostrophic equation. Under certain assumptions on the local geometric regularity of the level sets of $\theta$, we obtain global regularity results with improved growth estimate on $| \nabla^{\bot} \theta |$. We further perform numerical simulations to study the local geometric properties of the level sets near the region of maximum $| \nabla^{\bot} \theta |$. The numerical results indicate that the assumptions on the local geometric regularity of the level sets of $\theta$ in our theorems are satisfied. Therefore these theorems provide a good explanation of the double exponential growth of $| \nabla^{\bot} \theta |$ observed in this and past numerical simulations.
%U http://arxiv.org/abs/math/0601427v2