Equilibria of point-vortices on closed surfaces

2015/02/19 by Teresa D'Aprile, D'Aprile, Teresa, Pierpaolo Esposito +1
Mathematics · #35J20 #35J61 #35Q35 #76B47 #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP #msc:35J20 #msc:35J61 #msc:35Q35 #msc:76B47

paper · pdf · doi:10.48550/arxiv.1502.05579

27 pages

arxiv created 2015/02/19 · arxiv updated 2015/02/20

Abstract

We discuss the existence of equilibrium configurations for the Hamiltonian point-vortex model on a closed surface Σ. The topological properties of Σ determine the occurrence of three distinct situations, corresponding to \mathbbS², to \mathbbRP² and to Σ\not=\mathbbS²,\mathbbRP². As a by-product, we also obtain new existence results for the singular mean-field equation with exponential nonlinearity.

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