| Abstract: |
| We consider the two-dimensional Euler flow for an incompressible fluid confined to a smooth domain. We construct smooth solutions with concentrated vorticities around points which evolve according to the Hamiltonian system for the Kirkhoff-Routh energy. The profile around each point resembles a scaled finite mass solution of Liouville`s equation. We discuss extensions of this analysis to the case of vortex filaments in 3-dimensional space, along the lines of Da Rios 1904 vortex filament conjecture in connection with the binormal flow of curves. |
|