Level Set Dynamics and the Non-blowup of the 2D Quasi-geostrophic Equation TeX Export

@misc{citeulike:470453, abstract = {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.}, archivePrefix = {arXiv}, author = {Deng, Jian and Hou, Thomas Y. and Li, Ruo and Yu, Xinwei}, citeulike-article-id = {470453}, citeulike-linkout-0 = {http://arxiv.org/abs/math.AP/0601427}, citeulike-linkout-1 = {http://arxiv.org/pdf/math.AP/0601427}, day = {18}, eprint = {math.AP/0601427}, keywords = {2d, pde, quasi-geostrophic}, month = {Jan}, posted-at = {2006-01-19 10:40:45}, priority = {2}, title = {Level Set Dynamics and the Non-blowup of the 2D Quasi-geostrophic Equation}, url = {http://arxiv.org/abs/math.AP/0601427}, year = {2006} }

TY - ELEC ID - citeulike:470453 L3 - citeulike-article-id:470453 N2 - 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. TI - Level Set Dynamics and the Non-blowup of the 2D Quasi-geostrophic Equation KW - 2d KW - pde KW - quasi-geostrophic AU - Deng, Jian AU - Hou, Thomas AU - Li, Ruo AU - Yu, Xinwei PY - 2006/Jan/18/ UR - http://arxiv.org/abs/math.AP/0601427 ER -