Level Set Dynamics and the Non-blowup of the 2D Quasi-geostrophic Equation
| dc.creator | Deng, Jian | |
| dc.creator | Hou, Thomas Y. | |
| dc.creator | Li, Ruo | |
| dc.creator | Yu, Xinwei | |
| dc.date | 2006-01-18 | |
| dc.date | 2006-04-11 | |
| dc.date.accessioned | 2026-07-07T06:59:02Z | |
| dc.date.available | 2026-07-07T06:59:02Z | |
| dc.description | 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 $θ$, we obtain global regularity results with improved growth estimate on $| \nabla^{\bot} θ|$. We further perform numerical simulations to study the local geometric properties of the level sets near the region of maximum $| \nabla^{\bot} θ|$. The numerical results indicate that the assumptions on the local geometric regularity of the level sets of $θ$ in our theorems are satisfied. Therefore these theorems provide a good explanation of the double exponential growth of $| \nabla^{\bot} θ|$ observed in this and past numerical simulations. | |
| dc.description | 25 pages, 10 figures. Corrected a few typos | |
| dc.identifier | https://arxiv.org/abs/math/0601427 | |
| dc.identifier | http://arxiv.org/abs/math/0601427 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/107601 | |
| dc.subject | Analysis of PDEs | |
| dc.title | Level Set Dynamics and the Non-blowup of the 2D Quasi-geostrophic Equation | |
| dc.type | text |