Mathematics > Analysis of PDEs
[Submitted on 21 Dec 2018 (v1), last revised 24 Dec 2019 (this version, v2)]
Title:On stability of Euler flows on closed surfaces of positive genus
View PDFAbstract: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.
Submission history
From: Vladimir Yushutin Ph.D. [view email][v1] Fri, 21 Dec 2018 05:53:05 UTC (24 KB)
[v2] Tue, 24 Dec 2019 16:54:51 UTC (41 KB)
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