Deformation and Symmetry in the Inviscid SQG and the 3D Euler Equations

被引：10

作者：

Chae, Dongho ^{[2
]}

Constantin, Peter ^{[3
]}

Wu, Jiahong ^{[1
]}

机构：

[1] Oklahoma State Univ, Dept Math, Stillwater, OK 74078 USA

[2] Chung Ang Univ, Dept Math, Seoul 156756, South Korea

[3] Princeton Univ, Dept Math, Princeton, NJ 08544 USA

来源：

JOURNAL OF NONLINEAR SCIENCE | 2012年 / 22卷 / 05期

基金：

美国国家科学基金会;

关键词：

3D Euler equation; Surface quasi-geostrophic equation; Geometric property; BLOW-UP PROBLEM; BEHAVIOR; DYNAMICS;

D O I：

10.1007/s00332-012-9124-7

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The global regularity problem concerning the inviscid SQG and the 3D Euler equations remains an outstanding open question. This paper presents several geometric observations on solutions of these equations. One observation stems from a relation between what we call Eulerian and Lagrangian deformations and reflects the alignment of the stretching directions of these deformations and the tangent direction of the level curves for the SQG equation. Various spatial symmetries in solutions to the 3D Euler equations are exploited. In addition, two observations on the curvature of the level curves of the SQG equation are also included.

引用

页码：665 / 688

页数：24

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