Navier-Stokes regularity in 3D
General Physics
2014-02-12 v3
Abstract
This short proof shows that for smooth and sufficiently fast decaying initial data at infinity, the full incompressible Navier-Stokes solutions are eternal. The proof uses an orthogonal decomposition of the velocity field and some well-known vector calculus identities to establish a particular contradiction, which leads to a vanishing integral, which is the main integral that determines the evolution of enstrophy. As it is shown that enstrophy is non-increasing, it is well-know that the solutions stay regular at all times.
Keywords
Cite
@article{arxiv.1207.1090,
title = {Navier-Stokes regularity in 3D},
author = {Jussi Lindgren},
journal= {arXiv preprint arXiv:1207.1090},
year = {2014}
}