报告题目：Asymptotic analysis on the modelling of the shallow-water waves with the Coriolis effect

报告人：刘跃 教授 (University of Texas at Arlington)

主持人： 陈勇 教授

报告时间；2017年5月24日 15:00—16:00

报告地点：中北校区理科大楼B 1002室

报告人简介：

刘跃现为美国德克萨斯大学阿灵顿分校数学系的正教授，1994年博士毕业于美国布朗大学应用数学系，师从国际著名数学家Walter Strauss教授。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，他的研究兴趣在非线性波解的适定性、稳定性、长时间性态以及数值计算等。迄今刘跃教授已在CPAM, ARMA, CMP, Adv. Math, J. Reine Angew. Math., JMPA, JFA, CPDE, Math.Ann., Math.Z., TAMS, SIAM-JMA, JDE等国际著名刊物上发表论文90余篇。

报告摘要：

In this talk, a mathematical model of long-crested water waves propagating mainly in one direction with the effect of Earth's rotation is derived by following the formal asymptotic procedures. Such  a model equation is analogous to the Camassa-Holm approximation of the two-dimensional incompressible and  irrotational  Euler equations and has a formal bi-Hamiltonian structure.  Its solution corresponding to physically relevant initial perturbations is more accurate on a much longer time scale. It is shown that the deviation of the free surface can be determined by the horizontal velocity at a certain depth in the second-order approximation.  The  effects of the Coriolis force caused by the Earth rotation and  nonlocal higher nonlinearities on blow-up criteria and wave-breaking phenomena are also investigated. Our refined analysis is approached by applying the method of characteristics and conserved quantities to the  Riccati-type differential inequality.