Global nonlinear stability for steady ideal fluid flow in bounded planar domains

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Abstract

We prove stability of steady flows of an ideal fluid in a bounded, simply connected, planar region, that are strict maximisers or minimisers of kinetic energy on an isovortical surface. The proof uses conservation of energy and transport of vorticity for solutions of the vorticity equation with initial data in L-p for p > 4/3. A related stability theorem using conservation of angular momentum in a circular domain is also proved.
Original languageEnglish
Pages (from-to)149-163
Number of pages15
JournalArchive for Rational Mechanics and Analysis
Volume176
Issue number2
DOIs
Publication statusPublished - 2005

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