Deng, Jian; Hou, Thomas Y.; Yu, Xinwei A level set formulation for the 3D incompressible Euler equations. (English) Zbl 1107.76011 Methods Appl. Anal. 12, No. 4, 427-440 (2005). Summary: We explore a level set representation of vorticity in the study of singularity 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. Cited in 2 Documents MSC: 76B03 Existence, uniqueness, and regularity theory for incompressible inviscid fluids 35Q35 PDEs in connection with fluid mechanics Keywords:global existence; Clebsch representation; non-blowup PDF BibTeX XML Cite \textit{J. Deng} et al., Methods Appl. Anal. 12, No. 4, 427--440 (2005; Zbl 1107.76011) Full Text: DOI OpenURL