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

Deng, J. and Hou, T. Y. and Li, R. and Yu, X. (2006) Level Set Dynamics and the Non-blowup of the 2D Quasi-geostrophic Equation. . (Submitted) http://resolver.caltech.edu/CaltechAUTHORS:20160322-071936317

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Abstract

In this article we apply the technique proposed in Deng-Hou-Yu [7] 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 │∇^⊥θ│. We further perform numerical simulations to study the local geometric properties of the level sets near the region of maximum │∇^⊥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 │∇^⊥θ│ observed in this and past numerical simulations.


Item Type:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription
http://arxiv.org/abs/math/0601427arXivDiscussion Paper
Additional Information:Submitted on 18 Jan 2006 (v1), last revised 11 Apr 2006 (this version, v2). This work was in part supported by NSF under the NSF FRG grant DMS-0353838 and ITR Grant ACI-0204932.
Funders:
Funding AgencyGrant Number
NSFDMS-0353838
NSFACI-0204932
Record Number:CaltechAUTHORS:20160322-071936317
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20160322-071936317
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:65567
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:30 Mar 2016 23:59
Last Modified:30 Mar 2016 23:59

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