Critical Points of the $N$-vortex Hamiltonian in Bounded Planar Domains and Steady State Solutions of the Incompressible Euler Equations

DOI10.1137/140981253zbMath1317.35073arXiv1408.1748OpenAlexW1976575313MaRDI QIDQ5253657

Angela Pistoia, Thomas J. Bartsch

Publication date: 27 May 2015

Published in: SIAM Journal on Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1408.1748

zbMATH Keywords

vortex dynamicspoint vorticescounter-rotating vorticessteady states of Euler flow

Mathematics Subject Classification ID

Related Items (25)

Existence of steady multiple vortex patches to the vortex-wave system ⋮ Travelling helices and the vortex filament conjecture in the incompressible Euler equations ⋮ Periodic solutions of singular first-order Hamiltonian systems of \(N\)-vortex type ⋮ Sign-changing two-peak solutions for an elliptic free boundary problem related to confined plasmas ⋮ Periodic solutions with prescribed minimal period of vortex type problems in domains ⋮ Global continua of periodic solutions of singular first-order Hamiltonian systems of \(N\)-vortex type ⋮ Symmetric equilibria for the \(N\)-vortex problem ⋮ Existence of stationary vortex sheets for the 2D incompressible Euler equation ⋮ Equilibria of vortex type Hamiltonians on closed surfaces ⋮ Uniqueness, multiplicity and nondegeneracy of positive solutions to the Lane-Emden problem ⋮ Periodic solutions of the \(N\)-vortex Hamiltonian system in planar domains ⋮ Periodic Solutions of N-Vortex Type Hamiltonian Systems near the Domain Boundary ⋮ Desingularization of vortex rings in 3 dimensional Euler flows ⋮ Steady vortex patches with opposite rotation directions in a planar ideal fluid ⋮ Equilibria for the \(N\)-vortex-problem in a general bounded domain ⋮ Blow-up behavior for a degenerate elliptic \(\sinh \)-Poisson equation with variable intensities ⋮ Eight(y) mathematical questions on fluids and structures ⋮ Periodic solutions for the N-vortex problem via a superposition principle ⋮ Nonlinear stability of planar vortex patches in an ideal fluid ⋮ 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 ⋮ The number of positive solutions to the Brezis-Nirenberg problem ⋮ Stability of periodic solutions of the \(N\)-vortex problem in general domains ⋮ Gluing methods for vortex dynamics in Euler flows ⋮ Non-degeneracy and local uniqueness of positive solutions to the Lane-Emden problem in dimension two ⋮ Local uniqueness for vortex patch problem in incompressible planar steady flow

Cites Work

• 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
• Mathematical theory of incompressible nonviscous fluids
• On the existence of blowing-up solutions for a mean field equation
• Singular limits in Liouville-type equations
• Regularization of point vortices pairs for the Euler equation in dimension two
• Concentrating solutions for a planar elliptic problem involving nonlinearities with large exponent
• 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
• Vorticity and Incompressible Flow
• On the existence and profile of nodal solutions for a two-dimensional elliptic problem with large exponent in nonlinearity
• Point vortex dynamics: A classical mathematics playground
• Vortex Dynamics
• Existence and qualitative properties of concentrating solutions for the sinh-Poisson equation
• On the Motion of Vortices in Two Dimensions
• The \(N\)-vortex problem. Analytical techniques

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