Deformation and symmetry in the inviscid SQG and the 3D euler equations

Dongho Chae, Peter Constantin, Jiahong Wu

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

Abstract

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.

Original languageEnglish (US)
Pages (from-to)665-688
Number of pages24
JournalJournal of Nonlinear Science
Volume22
Issue number5
DOIs
StatePublished - Oct 1 2012

All Science Journal Classification (ASJC) codes

  • Modeling and Simulation
  • Engineering(all)
  • Applied Mathematics

Keywords

  • 3D Euler equation
  • Geometric property
  • Surface quasi-geostrophic equation

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