报告题目：Structural implication of constant vorticity to three-dimensional internal waves

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.

报告人简介：陈明，博士毕业于美国布朗大学数学系，师从著名数学家Walter Strauss教授，2011年到美国匹兹堡大学工作。陈明博士主要从事非线性偏微分方程的稳定性理论及行波解等问题的研究，工作涉及流体力学、地球物理和材料等领域中的偏微分方程，大量工作是研究解的全局正则性和奇点的形成。

报告时间：2024年07月25日 09:00-10:00

报告地点：同析4号楼 322会议室