Geometric Properties and Nonblowup of 3D Incompressible Euler Flow

By Jian Deng, Thomas Y. Hou, Xinwei Yu. 2004

136 citations recorded by the source corpus.

Abstract By exploring a local geometric property of the vorticity field along a vortex filament, we establish a sharp relationship between the geometric properties of the vorticity field and the maximum vortex stretching. This new understanding leads to an improved result of the global existence of the 3D Euler equation under mild assumptions.

Subfields: Applied Mathematics, Computational Mechanics

View Paper: https://www.semanticscholar.org/paper/862a838c4440fc76c1ac5614bc3e20b302cca17f

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Peter Constantin
2. Vlad Vicol
3. Luis Silvestre
4. Jiahong Wu
5. Pablo Raúl Stinga
6. Changxing Miao
7. Dong Li
8. Huy Quang Nguyen

In Computational Mechanics

1. Peter Constantin
2. Vlad Vicol
3. É. Mémin

Citations in the corpus

• On the Interior Regularity of Suitable Weak Solutions to the Navier–Stokes Equations (2007, unknown): “…equations we refer to Chae (2005, 2006a,b,c), while for the applications of the geometric structures of the ‘vortex stretching terms’ in the Euler equations and the quasi-geostrophic equations, we refer to Constantin (1994), Constantin et al. (1996), Deng et al. (2005), and references therein.”
• On the Euler equations of incompressible fluids (2007, background): “The criteria based on ξ have been extended and refined ([19], [69]) and validated numerically ([87]).”