Methods and Applications of Analysis

A Level Set Formulation for the 3D Incompressible Euler Equations

Jian Deng, Thomas Y. Hou, and Xinwei Yu

Full-text: Open access


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.

Article information

Methods Appl. Anal., Volume 12, Number 4 (2005), 427-440.

First available in Project Euclid: 5 April 2007

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 76B03: Existence, uniqueness, and regularity theory [See also 35Q35] 35Q35: PDEs in connection with fluid mechanics

Level sets Clebsch representation 3D Euler non-blowup


Deng, Jian; Hou, Thomas Y.; Yu, Xinwei. A Level Set Formulation for the 3D Incompressible Euler Equations. Methods Appl. Anal. 12 (2005), no. 4, 427--440.

Export citation