We discuss the existence of equilibrium configurations for the Hamiltonian point-vortex model on a closed surface Sigma. The topological properties of Sigma determine the occurrence of three distinct situations, corresponding to S^2, to RP^2 and to Sigma \not=S^2, RP^2. As a by-product, we also obtain new existence results for the singular mean-field equation with exponential nonlinearity.
D'Aprile, T., Esposito, P. (2017). Equilibria of point-vortices on closed surfaces. ANNALI DELLA SCUOLA NORMALE SUPERIORE DI PISA. CLASSE DI SCIENZE, 17(1), 287-321 [10.2422/2036-2145.201504_010].
Equilibria of point-vortices on closed surfaces
ESPOSITO, PIERPAOLO
2017-01-01
Abstract
We discuss the existence of equilibrium configurations for the Hamiltonian point-vortex model on a closed surface Sigma. The topological properties of Sigma determine the occurrence of three distinct situations, corresponding to S^2, to RP^2 and to Sigma \not=S^2, RP^2. As a by-product, we also obtain new existence results for the singular mean-field equation with exponential nonlinearity.File in questo prodotto:
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