Some stability problems to the Navier-Stokes equations in the periodic case
Analysis of PDEs
2016-06-16 v1
Abstract
The Navier-Stokes motions in a box with periodic boundary conditions are considered. First the existence of global regular two-dimensional solutions is proved. The solutions are such that continuous with respect to time norms are controlled by the same constant for all . Assuming that the initial velocity and the external force are sufficiently close to the initial velocity and the external force of the two-dimensional solutions we prove existence of global three-dimensional regular solutions which remain close to the two-dimensional solutions for all time. In this way we mean stability of two-dimensional solutions.
Cite
@article{arxiv.1606.04701,
title = {Some stability problems to the Navier-Stokes equations in the periodic case},
author = {Wojciech M. Zajaczkowski},
journal= {arXiv preprint arXiv:1606.04701},
year = {2016}
}
Comments
arXiv admin note: substantial text overlap with arXiv:1510.04002, arXiv:1406.0693