报告题目：Stability of peakons of the shallow water modeling with cubic nonlinearity
报 告人：刘跃 美国德州大学阿灵顿分校
Abstract: In the present talk, we derive a simplified phenomenological model of shallow-water wave propagating mainly in the equatorial ocean regions with the Coriolis effect caused by the Earth's rotation. The model equation which is analogous to the Green-Naghdi equations with the second-order approximation of the Camassa-Holm scaling captures stronger nonlinear effects than the classical dispersive integrable
equations like the Korteweg-de Vries and two-component Camassa-Holm system. The local well-posedness of the Cauchy problem is then established by the linear transport theory and wave-breaking phenomena is investigated based on the method of characteristics and the Riccati type differential inequality. Finally, the condition of permanent waves is demonstrated by analyzing competition between the slope of average of horizontal velocity component and the free surface component.
主讲人介绍：刘跃，1994年博士毕业于美国布朗大学，主要从事非线性水波模型问题的研究，在一大类浅水波模型的推导，分析，稳定性方面做出了许多国际一流的工作。其研究成果发表在《Comm. Pure Appl. Math.》, 《Adv. Math.》, 《Comm. Math. Phys.》,
《Arch. Ration.Mech. Anal.》, 《J. Funct. Anal.》等国际著名刊物上。