Computer simulations for the blow-up of complex solutions of the 3-d Navier-Stokes equations
Fluid Dynamics
2017-02-16 v1 Numerical Analysis
Abstract
We present a study by computer simulations of a class of complex-valued solutions of the three-dimensional Navier-Stokes equations in the whole space, which, according to Li and Sinai, present a blow-up (singularity) at a finite time. The computer results allow a detailed study of the blow-up mechanism, and show interesting features of the behavior of the solutions near the blow-up time, such as the concentration of energy and enstrophy in a small region around a few points of physical space, while outside this region the "fluid" remains "quiet".
Keywords
Cite
@article{arxiv.1702.04503,
title = {Computer simulations for the blow-up of complex solutions of the 3-d Navier-Stokes equations},
author = {Carlo Boldrighini and Sandro Frigio and Pierluigi Maponi},
journal= {arXiv preprint arXiv:1702.04503},
year = {2017}
}