English

A bounded numerical solution with a small mesh size implies existence of a smooth solution to the Navier-Stokes equations

Analysis of PDEs 2020-11-12 v3 Numerical Analysis Numerical Analysis

Abstract

We prove that for a given smooth initial value, if the finite element solution of the three-dimensional Navier-Stokes equations is bounded in a certain norm with a relatively small mesh size, then the solution of the Navier-Stokes equations with this given initial value must be smooth and unique, and is successfully approximated by the numerical solution.

Keywords

Cite

@article{arxiv.1411.2253,
  title  = {A bounded numerical solution with a small mesh size implies existence of a smooth solution to the Navier-Stokes equations},
  author = {Buyang Li},
  journal= {arXiv preprint arXiv:1411.2253},
  year   = {2020}
}