We consider the two-dimensional Euler flow for an incompressible fluid confined to a smooth domain. We construct smooth solutions with concentrated vorticities around k points which evolve according to the Hamiltonian system for the Kirchhoff-Routh energy, using an outer-inner solution gluing approach.
The asymptotically singular profile around each point resembles a scaled finite mass solution of Liouville's equation. We also discuss the vortex filament conjecture for the three-dimensional case. This is joint work with Juan Dávila, Monica Musso and Juncheng Wei.