Generic hydrodynamic instability of curl eigenfields
Dynamical Systems
2007-05-23 v1 Symplectic Geometry
Abstract
We prove that for generic geometry, the curl-eigenfield solutions to the steady Euler equations on the three torus are all hydrodynamically unstable (linear, L^2 norm). The proof involves a marriage of contact topological methods with the instability criterion of Friedlander-Vishik. An application of contact homology is the crucial step.
Cite
@article{arxiv.math/0306310,
title = {Generic hydrodynamic instability of curl eigenfields},
author = {John B. Etnyre and Robert Ghrist},
journal= {arXiv preprint arXiv:math/0306310},
year = {2007}
}