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

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.

arXiv comment21 pages

Cited by in corpus (5)

• Computing Nearly Singular Solutions Using Pseudo-Spectral Methods
• Dynamic Depletion of Vortex Stretching and Non-Blowup of the 3-D Incompressible Euler Equations
• Numerical simulations of possible finite time singularities in the incompressible Euler equations: comparison of numerical methods
• Finite Time Blow-up of a 3D Model for Incompressible Euler Equations
• On Finite Time Singularity and Global Regularity of an Axisymmetric Model for the 3D Euler Equations