Methods and Applications of Analysis
Volume 12 (2005)
A Level Set Formulation for the 3D Incompressible Euler Equations
Pages: 427 – 440
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