Steady Contiguous Vortex-Patch Dipole Solutions of the 2D Incompressible Euler Equation
发布时间：2024年09月23日
浏览次数：289
发布者: He Liu
主讲人： 童嘉骏（北京大学）
活动时间： 从 2024-10-28 16:00 到 17:00
场地： 智华楼四元厅
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.
