Inviscid Models Generalizing the Two-dimensional Euler and the Surface Quasi-geostrophic Equations
- Authors
- Chae, Dongho; Constantin, Peter; Wu, Jiahong
- Issue Date
- Oct-2011
- Publisher
- SPRINGER
- Citation
- ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, v.202, no.1, pp 35 - 62
- Pages
- 28
- Journal Title
- ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS
- Volume
- 202
- Number
- 1
- Start Page
- 35
- End Page
- 62
- URI
- https://scholarworks.bwise.kr/cau/handle/2019.sw.cau/57064
- DOI
- 10.1007/s00205-011-0411-5
- ISSN
- 0003-9527
1432-0673
- Abstract
- Any classical solution of the two-dimensional incompressible Euler equation is global in time. However, it remains an outstanding open problem whether classical solutions of the surface quasi-geostrophic (SQG) equation preserve their regularity for all time. This paper studies solutions of a family of active scalar equations in which each component u(j) of the velocity field u is determined by the scalar theta through u(j) = R Lambda P-1(Lambda)theta, where R is a Riesz transform and Lambda = (-Delta)(1/2). The two-dimensional Euler vorticity equation corresponds to the special case P(Lambda) = I while the SQG equation corresponds to the case P(Lambda) = Lambda. We develop tools to bound parallel to del u parallel to(L infinity) for a general class of operators P and establish the global regularity for the Loglog-Euler equation for which P(Lambda) = (log(I + log(I - Delta)))(gamma) with 0 <= gamma <= 1. In addition, a regularity criterion for the model corresponding to P(Lambda) = Lambda(beta) with 0 <= beta <= 1 is also obtained.
- Files in This Item
- There are no files associated with this item.
- Appears in
Collections - College of Natural Sciences > Department of Mathematics > 1. Journal Articles
![qrcode](https://api.qrserver.com/v1/create-qr-code/?size=55x55&data=https://scholarworks.bwise.kr/cau/handle/2019.sw.cau/57064)
Items in ScholarWorks are protected by copyright, with all rights reserved, unless otherwise indicated.