On stability of Euler flows on closed surfaces of positive genus
Analysis of PDEs
2019-12-25 v2 Mathematical Physics
math.MP
Abstract
Incompressible flows of an ideal two-dimensional fluid on a closed orientable surface of positive genus are considered. Linear stability of harmonic, i.e. irrotational and incompressible, solutions to the Euler equations is shown using the Hodge-Helmholtz decomposition. We also demonstrate that any surface Euler flow is stable with respect to harmonic velocity perturbations.
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Cite
@article{arxiv.1812.08959,
title = {On stability of Euler flows on closed surfaces of positive genus},
author = {Vladimir Yushutin},
journal= {arXiv preprint arXiv:1812.08959},
year = {2019}
}
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5 pages