Desingularization of V-states

Vortrag von Razvan-Octavian Radu

Datum: 30.10.25  Zeit: 17.00 - 18.00  Raum: ETH HG G 19.2

V-states are uniformly rotating vortex patch solutions to the 2D Euler equations. Namely, the vorticity is given by the characteristic function of a domain which rotates around the origin with constant angular velocity. Examples of V-states include Kirchhoff ellipses and m-fold symmetric patches which bifurcate from the disk. I will describe how, for any V-state satisfying a certain non-degeneracy condition, there exist smooth rigidly rotating solutions to the 2D Euler equations approximating it arbitrarily well in the natural Hölder spaces. I will then argue that all but countably many Kirchhoff ellipses, as well as all m-fold symmetric V-states near the disk satisfy this non-degeneracy.