报告人：刘跃（美国德克萨斯⼤学阿灵顿分校）

邀请人：李骥

报告时间：2023年6月20日（星期二）9:00-10:30

报告地点：科技楼南楼705室

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

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.

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, 发表在《Comm. Pure Appl. Math.》, 《Ann. PDE》, 《J. Reine Angew. Math.》, 《J. Math. Pures Appl.》，《Adv. Math.》, 《Comm. Math. Phys.》, 《Arch. Ration. Mech. Anal.》, 《Math. Ann.,》，《J. Funct. Anal.》, 《Int. Math. Res. Not.,》，《Trans. AMS》等国际著名刊物上。