学 术 报 告
报告题目： On the Camassa-Holm-KP model arising in shallow water theory
报告时间：2020年10月17日（周六） 上午 9：00-10：30
报告形式：腾讯会议 会议ID：660 926 130
主讲专家：刘跃 教授/博导 美国德克萨斯大学阿灵顿分校
报告摘要：In this talk we describe the asymptotic perturbation method to derive a two-dimensional Camassa-Holm-Kadomtsev-Petviashvili-type equation in the context of full water waves. Starting from the incompressible and irrotational governing equations in the three-dimensional water waves, we show that such a equation arises in the modeling of the propagation of shallow water waves over a flat bed. The resulting equation is a two dimensional Camassa-Holm equation with weakly transverse effect for the horizontal velocity component. The equation captures stronger nonlinear effects than the classical dispersive integrable equations like the Korteweg-de Vries and Kadomtsev-Petviashvili equations. We also address some properties of the this model equation and how it relates to the surface wave. Finally, we investigate the formation of singularities and the existence of peaked traveling-wave solutions of the model equation.
专家介绍：刘跃，美国德克萨斯大学阿灵顿分校数学系教授。研究专长：非线性波解的适定性、稳定性、长时间性态以及数值计算等。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学者。