Steady Contiguous Vortex-Patch Dipole Solutions of the 2D Incompressible Euler Equation
报告人：童嘉骏 （welcome欢迎光临威尼斯公司）
时间：2024-10-28 16:00-17:00
地点：智华楼313
Abstract: It is of great mathematical and physical interest to study traveling wave solutions to the 2D incompressible Euler equation in the form of a touching pair of symmetric vortex patches with opposite signs. Such a solution was numerically illustrated by Sadovskii in 1971, but its rigorous existence was left as an open problem. In this talk, we will rigorously construct such a solution by a novel fixed-point approach that determines the patch boundary as a fixed point of a nonlinear map. Smoothness and other properties of the patch boundary will also be characterized. This is based on a joint work with De Huang.
