Steady Contiguous Vortex-Patch Dipole Solutions of the 2D Incompressible Euler Equation
Time: 2024-09-23
Published By: He Liu
Speaker(s): Jiajun Tong(Peking University)
Time: 16:00-17:00 October 28, 2024
Venue: Siyuan Lecture Hall, Zhihua Building
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.
