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.
"A Level Set Formulation for the 3D Incompressible Euler Equations." Methods Appl. Anal. 12 (4) 427 - 440, December 2005.