Steady Contiguous Vortex-Patch Dipole Solutions of the 2D Incompressible Euler Equation
Prof. Jiajun TONG
Date & Time
07 Jan 2025 (Tue) | 04:00 PM - 05:00 PM
Venue
Y5-205, Yeung Kin Man Academic Building
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.