Title: Desingularization of the Hill-Norbury family of steady vortex rings
Abstract: In 1894, Hill found an explicit traveling-wave solution of the three-dimensional incompressible Euler equations whose vorticity is supported in a ball. In 1972, Norbury constructed a family of nearby traveling waves with toroidal vorticity support. These solutions have discontinuous relative vorticity, equal to a constant multiple of the characteristic function of the vortex core. I will present a desingularization method for constructing smooth, steady vortex ring solutions approximating the Hill-Norbury family in the natural topology. This is joint work with Noah Stevenson.