Trapping Regions for the Navier-Stokes Equations
Abstract
In 1999, J.C. Mattingly and Ya. G. Sinai used elementary methods to prove the existence and uniqueness of smooth solutions to the 2D Navier-Stokes equations with periodic boundary conditions. And they were almost successful in proving the existence and uniqueness of smooth solutions to the 3D Navier-Stokes equations using the same strategy. In this paper, we modify their technique to obtain a simpler proof of one of their results. We also argue that there is no logical reason why the 3D Navier-Stokes equations must always have solutions, even when the initial velocity vector field is smooth; if they do always have solutions, it is due to probability and not logic.
Keywords
Cite
@article{arxiv.math/0404302,
title = {Trapping Regions for the Navier-Stokes Equations},
author = {Craig Alan Feinstein},
journal= {arXiv preprint arXiv:math/0404302},
year = {2014}
}
Comments
4 pages. arXiv admin note: text overlap with arXiv:math/9903042 by other authors