Equilibria of vortex type Hamiltonians on closed surfaces

DOI10.12775/tmna.2023.003zbMath1521.37080arXiv2203.13566MaRDI QIDQ6044509

No author found.

Publication date: 19 May 2023

Published in: Topological Methods in Nonlinear Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2203.13566

zbMATH Keywords

blow-up solutionssinh-Poisson equationmean field equationspoint vortex equilibriacounter-rotating vorticespoint vortex Hamiltonian

Mathematics Subject Classification ID

Vortex flows for incompressible inviscid fluids (76B47) Nonlinear elliptic equations (35J60) Stability problems for infinite-dimensional Hamiltonian and Lagrangian systems (37K45) Second-order elliptic equations (35J15) Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with topology, geometry and differential geometry (37K25) Blow-up in context of PDEs (35B44) PDEs on manifolds (35R01) Relations of finite-dimensional Hamiltonian and Lagrangian systems with topology, geometry and differential geometry (symplectic geometry, Poisson geometry, etc.) (37J39)

Cites Work

• Unnamed Item
• Unnamed Item
• Periodic solutions of singular first-order Hamiltonian systems of \(N\)-vortex type
• Sign-changing blow-up solutions for Hénon type elliptic equations with exponential nonlinearity
• Equilibria for the \(N\)-vortex-problem in a general bounded domain
• Theory of ``critical points at infinity and a resonant singular Liouville-type equation
• On a resonant mean field type equation: a ``critical point at infinity approach
• Singular mean field equations on compact Riemann surfaces
• The principle of symmetric criticality
• Symmetric equilibria for the \(N\)-vortex problem
• Periodic solutions of the \(N\)-vortex Hamiltonian system in planar domains
• \(N\)-vortex equilibria for ideal fluids in bounded planar domains and new nodal solutions of the sinh-Poisson and the Lane-Emden-Fowler equations
• Periodic solutions for the N-vortex problem via a superposition principle
• Singular limits in Liouville-type equations
• Global continua of periodic solutions of singular first-order Hamiltonian systems of \(N\)-vortex type
• Singular limits for Liouville-type equations on the flat two-torus
• Vorticity and Incompressible Flow
• Multiple Blow-Up Solutions for the Liouville Equation with Singular Data
• Vortices on Closed Surfaces
• Vortex motion on surfaces with constant curvature
• Topological degree for a mean field equation on Riemann surfaces
• Periodic solutions with prescribed minimal period of vortex type problems in domains
• Equilibria of point-vortices on closed surfaces
• Morse inequalities at infinity for a resonant mean field equation
• Critical Points of the $N$-vortex Hamiltonian in Bounded Planar Domains and Steady State Solutions of the Incompressible Euler Equations
• Nontopological Condensates for the Self‐Dual Chern‐Simons‐Higgs Model
• Vortex Dynamics
• The motion of point vortices on closed surfaces
• Point vortex interactions on a toroidal surface
• Existence and qualitative properties of concentrating solutions for the sinh-Poisson equation
• The \(N\)-vortex problem. Analytical techniques

This page was built for publication: Equilibria of vortex type Hamiltonians on closed surfaces