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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 Lp for p>4/3. A related stability theorem using conservation of angular momentum in a circular domain is also proved.

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Authors and Affiliations

  1. Department of Mathematical Sciences, University of Bath, Claverton Down, Bath, BA2 7AY, U.K

    G.R. Burton

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  1. G.R. Burton
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Correspondence to G.R. Burton.

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Communicated by V. Šverák

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Burton, G. Global Nonlinear Stability for Steady Ideal Fluid Flow in Bounded Planar Domains. Arch. Rational Mech. Anal. 176, 149–163 (2005). https://doi.org/10.1007/s00205-004-0339-0

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  • DOI: https://doi.org/10.1007/s00205-004-0339-0

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