Vorticity Direction and Regularity of Solutions to the Navier-Stokes Equations

  • Hugo Beirão da Veiga
  • Yoshikazu Giga
  • Zoran Grujić
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Abstract

It has been well documented – both in computational simulations of the 3D Navier-Stokes equations and the experiments with 3D incompressible turbulent fluid flows – that the regions of intense vorticity self-organize in coherent vortex structures, most notably, vortex filaments. One of the morphological characteristics of these structures is local coherence of the vorticity direction. The goal of this chapter is to review several avenues taken by the mathematical fluids community in order to study how the local coherence of the vorticity direction – a purely geometric condition – influences the possible formation of singularities in solutions to the 3D Navier-Stokes equations.

Keywords

Mild Solution Anisotropic Diffusion Regularity Criterion Vortex Filament Local Coherence 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Hugo Beirão da Veiga
    • 1
  • Yoshikazu Giga
    • 2
  • Zoran Grujić
    • 3
  1. 1.Dipartimento di MatematicaUniversità di PisaPisaItaly
  2. 2.Graduate School of Mathematical SciencesUniversity of TokyoMeguro, TokyoJapan
  3. 3.Department of MathematicsUniversity of VirginiaCharlottesvilleUSA

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