| Abstract: |
| In this talk, we will present new results on the existence of periodic configurations of hollow vortices. A hollow vortex is a region of constant pressure bounded by a vortex sheet and suspended inside a fluid, whose flow is governed by the 2D Euler equations. We will show that there exists a one-parameter family of steady, periodic hollow vortices that bifurcates from a periodic point vortex configuration and extends up to the onset of certain singularities, which we also classify. Some notable applications are the existence of von K\'{a}rm\'{a}n, and 2P, hollow vortex streets. The technique involves reformulating the problem using complex analysis tools, including conformal mappings and layer potential representations, then carrying out a global bifurcation argument. |
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