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- W2045512504 abstract "We prove the existence of equilibria of the N-vortex Hamiltonian in a bounded domain ({Omegasubsetmathbb{R}^2}) , which is not necessarily simply connected. On an arbitrary bounded domain we obtain new equilibria for N = 3 or N = 4. If Ω has an axial symmetry we obtain a symmetric equilibrium for each ({Ninmathbb{N}}) . We also obtain new stream functions solving the sinh-Poisson equation ({-Deltapsi=rhosinhpsi}) in Ω with Dirichlet boundary conditions for ρ > 0 small. The stream function ({psi_rho}) induces a stationary velocity field ({v_rho}) solving the Euler equation in Ω. On an arbitrary bounded domain we obtain velocitiy fields having three or four counter-rotating vortices. If Ω has an axial symmetry we obtain for each N a velocity field ({v_rho}) that has a chain of N counter-rotating vortices, analogous to the Mallier-Maslowe row of counter-rotating vortices in the plane. Our methods also yield new nodal solutions for other semilinear Dirichlet problems, in particular for the Lane-Emden-Fowler equation ({-Delta u=|u|^{p-1}u}) in Ω with p large." @default.
- W2045512504 created "2016-06-24" @default.
- W2045512504 creator A5051030991 @default.
- W2045512504 creator A5062208839 @default.
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- W2045512504 date "2014-11-26" @default.
- W2045512504 modified "2023-09-26" @default.
- W2045512504 title "Erratum to: N-Vortex Equilibria for Ideal Fluids in Bounded Planar Domains and New Nodal Solutions of the sinh-Poisson and the Lane-Emden-Fowler Equations" @default.
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- W2045512504 doi "https://doi.org/10.1007/s00220-014-2230-7" @default.
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