Level Set Dynamics and the Nonblowup of the 2D Quasigeostrophic Equation
Abstract
In this article we apply the technique proposed in DengHouYu (Comm. PDE, 2005) to study the level set dynamics of the 2D quasigeostrophic 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.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 January 2006
 arXiv:
 arXiv:math/0601427
 Bibcode:
 2006math......1427D
 Keywords:

 Mathematics  Analysis of PDEs
 EPrint:
 25 pages, 10 figures. Corrected a few typos