Vortrag: "The $N$-vortex problem -- Periodic solutions in bounded domains"

Abstract: We will discuss the existence of nonstationary collision-free periodic solutions for the $N$-vortex problem on general domains $\Omega\subset\mathbb{R}^2$. The problem in question is a first order Hamiltonian system arising as a singular limit (not only) in two-dimensional fluid dynamics. The Hamiltonian contains logarithmic singularities and is except for some special domains not explicitly known.
The talk will provide an overview of available results with an emphasis on choreographic solutions that can be found near the boundary of the domain.