Speaker：Changjun Zou(Sichuan University)

Time：2022-10-20, 15:00

Location：Tencent Meeting ID：406 883 552（No Password）

Abstract:

We will talk about steady vortex rings in an ideal fluid of uniform density, which are special global solutions of the three-dimensional incompressible Euler equation. We systematically establish the existence, uniqueness and nonlinear stability of steady vortex rings of small cross-section for which the potential vorticity is constant throughout the core. The latter two answer a long-standing question since the pioneering work of Fraenkel and Berger (Acta Math 132:13--51, 1974). Our proof is based on a combination of the Lyapunov-Schmidt reduction argument, the local Pohozaev identity technique and the variational method, which provides a general approach for a large class of thin vortex rings.