Methods and Applications of Analysis

Volume 12 (2005)

Number 4

A Level Set Formulation for the 3D Incompressible Euler Equations

Pages: 427 – 440



Jian Deng

Thomas Y. Hou

Xinwei Yu


We explore a level set representation of vorticity in the study of the singularity problems for incompressible fluid models. This representation exists for all initial vorticity fields. We further apply it to study the 3D Lagrangian averaged Euler equations and the 3D Euler equations, and obtain new global existence conditions.


Level sets; Clebsch representation; 3D Euler; non-blowup

2010 Mathematics Subject Classification

35Q35, 76B03

Published 1 January 2005