Geometric properties and non-blowup of 3-D incompressible Euler flow

2004/02/12 by Jian Deng, Thomas Y. Hou, Deng, Jian +3 · 1 citation
Engineering · Mathematics · Physics and Astronomy · #Computational Fluid Dynamics and Aerodynamics #Fluid Dynamics and Turbulent Flows #Tribology and Lubrication Engineering #math-ph #math.MP #msc:76B03

paper · pdf · doi:10.48550/arxiv.math-ph/0402032

21 pages

arxiv created 2004/02/12 · arxiv updated 2009/12/01

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 3-D Euler equation under mild assumptions that are consistent with the observations from recent numerical computations.

Cited by

• On Finite Time Singularity and Global Regularity of an Axisymmetric Model for the 3D Euler Equations

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