Flexibility and rigidity in steady fluid motion
Analysis of PDEs
2021-03-31 v2 Fluid Dynamics
Abstract
Flexibility and rigidity properties of steady (time-independent) solutions of the Euler, Boussinesq and Magnetohydrostatic equations are investigated. Specifically, certain Liouville-type theorems are established which show that suitable steady solutions with no stagnation points occupying a two-dimensional periodic channel, or axisymmetric solutions in (hollowed out) cylinder, must have certain structural symmetries. It is additionally shown that such solutions can be deformed to occupy domains which are themselves small perturbations of the base domain. As application of the general scheme, Arnol'd stable solutions are shown to be structurally stable.
Cite
@article{arxiv.2007.09103,
title = {Flexibility and rigidity in steady fluid motion},
author = {Peter Constantin and Theodore D. Drivas and Daniel Ginsberg},
journal= {arXiv preprint arXiv:2007.09103},
year = {2021}
}
Comments
35 pages, 3 figures