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

报告人：Yue Liu 教授，University of Texas at Arlington.

时间：2017年6月30日星期五10:30-11:30

地点：清水河主楼A1-512

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.

报告人简介：刘跃，美国德克萨斯大学阿灵顿分校数学系教授，1994年博士毕业于美国布朗大学数学系，师从国际著名数学家Walter Strauss教授，其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，是国际上偏微分方程研究尤其是浅水波领域的一流专家，目前已在CPAM, CMP, ARMA, Adv. Math, J. Reine Angew.Math., JMPA, Math.Ann.,Math.Z.,JFA, CPDE, TAMS, Nonlinearity与 JDE等国际著名刊物上发表论文90余篇，是国际上非线性发展方程理论研究领域的权威专家。