Vortex reconnection in the three dimensional Navier-Stokes equations
Analysis of PDEs
2016-06-24 v2
Abstract
We prove that the vortex structures of solutions to the 3D Navier-Stokes equations can change their topology without any loss of regularity. More precisely, we construct smooth high-frequency solutions to the Navier-Stokes equations where vortex lines and vortex tubes of arbitrarily complicated topologies are created and destroyed in arbitrarily small times. This instance of vortex reconnection is structurally stable and in perfect agreement with the existing computer simulations and experiments. We also provide a (non-structurally stable) scenario where the destruction of vortex structures is instantaneous.
Keywords
Cite
@article{arxiv.1606.06176,
title = {Vortex reconnection in the three dimensional Navier-Stokes equations},
author = {Alberto Enciso and Renato Luca and Daniel Peralta-Salas},
journal= {arXiv preprint arXiv:1606.06176},
year = {2016}
}