Speaker：Daoming Cao (AMSS, CAS)

Time：2025-11-27 15:30

Location：Conference Room S102 at Experiment Building at Haiyun Campus

Abstract:

M-fold symmetric vortex patch solutions form a particularly important class of vortex solutions for the incompressible Euler equations. In the two-dimensional case, numerous results exist. For example, the characteristic function of a disk centered at the origin represents a trivial vortex patch solution. Another well-known example is the Kirchhoff vortex patch, which corresponds to the characteristic function of an elliptical domain. For the three-dimensional incompressible Euler equations, however, while several results have been established for solutions with vorticity highly concentrated along helically symmetric curves (featuring small cross-sections), helical symmetric solutions with large cross-sections remain scarce. This talk presents joint work in which the Crandall–Rabinowitz bifurcation theorem is applied to prove the existence of m-fold symmetric helical vortex patch solutions (also known as m-fold Kelvin waves), whose cross-sections approximate disks. This talk is based on joint work with Boquan Fan, Rui Li, and Guolin Qin.