Blowup or no blowup? The interplay between theory and numerics

The question of whether the 3D incompressible Euler equations can develop a finite time singularity from smooth initial data has been an outstanding open problem in fluid dynamics and mathematics. Recent studies indicate that the local geometric regularity of vortex lines can lead to dynamic depletion of vortex stretching. Guided by the local non-blowup theory, we have performed large scale computations of the 3D Euler equations on some of the most promising blowup candidates. Our results show that there is tremendous dynamic depletion of vortex stretching. The local geometric regularity of vortex lines and the anisotropic solution structure play an important role in depleting the nonlinearity dynamically and thus prevents a finite time blowup. (C) 2008 Elsevier B.V. All rights reserved.