Structural implication of constant vorticity to three-dimensional internal waves
数学专题报告
报告题目(Title)：Structural implication of constant vorticity to three-dimensional internal waves
报告人(Speaker)：Professor Chen,Robin Ming （University of Pittsburgh）
地点(Place)：后主楼 1223
时间(Time)：2024年 7 月 9 日（周二） 10:00--11:00
邀请人(Inviter)：李海刚
报告摘要
It is known that in many physical regimes, water waves beneath vacuum that have constant vorticity are necessarily two dimensional. The situation is more subtle for internal waves that traveling along the interface between two immiscible fluids. When the layers have the same density, there is a large class of explicit steady waves with constant vorticity that are three-dimensional in that the velocity field is pointing in one horizontal direction while the interface is an arbitrary function of the other horizontal variable. We prove that every three-dimensional traveling internal wave with bounded velocity for which the vorticities in the upper and lower layers are nonzero, constant, and parallel must belong to this family. If the densities in each layer are distinct, then in fact the flow is fully two dimensional. This is a joint work with Lili Fan, Samuel Walsh, and Miles Wheeler.
