Deng, Jian and Hou, Thomas Y. and Yu, Xinwei (2006) Improved Geometric Conditions for Non-Blowup of the 3D Incompressible Euler Equation. Communications in Partial Differential Equations, 31 (2). pp. 293-306. ISSN 0360-5302. doi:10.1080/03605300500358152. https://resolver.caltech.edu/CaltechAUTHORS:20170408-133541409
Full text is not posted in this repository. Consult Related URLs below.
Use this Persistent URL to link to this item: https://resolver.caltech.edu/CaltechAUTHORS:20170408-133541409
Abstract
This is a follow-up of our recent article Deng et al. (2004 Deng, J.,Hou, T. Y., Yu, X. (2004). ). In Deng et al. (2004), we derive some local geometric conditions on vortex filaments which can prevent finite time blowup of the 3D incompressible Euler equation. In this article, we derive improved geometric conditions which can be applied to the scenario when velocity blows up at the same time as vorticity and the rate of blowup of velocity is proportional to the square root of vorticity. This scenario is in some sense the worst possible blow-up scenario for velocity field due to Kelvin's circulation theorem. The improved conditions can be checked by numerical computations. This provides a sharper local geometric constraint on the finite time blowup of the 3D incompressible Euler equation.
| Item Type: | Article | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Related URLs: |
| |||||||||
| Additional Information: | © 2006 Taylor & Francis Group. Received October 1, 2004; Accepted August 1, 2005. This work was supported in part by NSF under the grant DMS-0073916 and ITR grant ACI-0204932. | |||||||||
| Funders: |
| |||||||||
| Subject Keywords: | 3D Euler equations, Finite time blowup, Geometric properties, Global existence | |||||||||
| Issue or Number: | 2 | |||||||||
| Classification Code: | Mathematics Subject Classification: Primary 76B03, Secondary 35L60, 35M10 | |||||||||
| DOI: | 10.1080/03605300500358152 | |||||||||
| Record Number: | CaltechAUTHORS:20170408-133541409 | |||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20170408-133541409 | |||||||||
| Official Citation: | Jian Deng , Thomas Y. Hou & Xinwei Yu (2006) Improved Geometric Conditions for Non-Blowup of the 3D Incompressible Euler Equation, Communications in Partial Differential Equations, 31:2, 293-306, DOI: 10.1080/03605300500358152 | |||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | |||||||||
| ID Code: | 75864 | |||||||||
| Collection: | CaltechAUTHORS | |||||||||
| Deposited By: | 1Science Import | |||||||||
| Deposited On: | 13 Apr 2017 19:40 | |||||||||
| Last Modified: | 15 Nov 2021 16:55 |
Repository Staff Only: item control page
