Existence and stability of a Sadovskii dipole as a maximizer of kinetic energy

Speaker: Prof. Kyudong Choi (Ulsan National Institute of Science and Technology, Korea)

Inviter: 王益 研究员

Title: Existence and stability of a Sadovskii dipole as a maximizer of kinetic energy

Time & Venue: 2025.6.25 15:30-16:30  南楼620

Abstract: The Sadovskii vortex patch is a traveling wave for the two-dimensional incompressible Euler equations consisting of an odd symmetric pair of vortex patches touching the symmetry axis. Its existence was first suggested by numerical computations of Sadovskii in [J. Appl. Math. Mech., 1971], and has gained significant interest due to its relevance in the inviscid limit of planar flows via Prandtl--Batchelor theory and as the asymptotic state for vortex ring dynamics.In this talk, I will sketch a proof of the existence of such a vortex and stability in the class using an energy maximization approach under the exact impulse condition and an upper bound on the circulation. (For reference, a completely different proof of the same existence result with more information via a fixed point method appeared around the same time by Huang and Tong. The uniqueness of such a vortex remains open.) This talk is based on joint work with In-Jee Jeong(SNU), Youngjin Sim(UNIST), and Kwan Woo(SNU).