报告题目：Asymptotic Model Equations Arising in Shallow Water Theory

报 告 人：刘跃 教授

主 持 人：陈勇 教授

报告时间：2018年7月3日 周二 10:00-11:00

报告地点：中北校区数学馆东202

报告人简介：

刘跃，美国德克萨斯大学阿灵顿分校教授，1994年获布朗大学博士学位。刘跃教授是目前国际上偏微分方程研究尤其是浅水波领域的一流专家。在偏微分方程，应用分析和流体力学，可积系统与孤子理论，非线性波方程的稳定性理论、奇异性形成、局部和整体适定性等领域取得国际领先的成果。在《Physica D》、《J. Differential Equations》、《Nonlinearity》、《Quart. of Appl. Math.》等国际重要刊物上发表论文80余篇。

报告摘要：

The study of water waves has a long history starting from Euler in 1752, and continues to be a very active area to the present day. Mathematically, the water wave equations describe the motion of water bounded above by a free surface. This free surface is subject to a constant (atmospheric) pressure, while gravity acts as an external force. In this talk, I will start by demonstrating the underlying complexity of the physical system,  and then I will  discuss possible simplifications in the "shallow water" regime along with the relevant physical phenomena. In particular, I will focus on the singularity formation of the Cauchy problem for the simplified nonlocal shallow-water models, such as Camassa-Holm-type equations in 1D and 2D cases.