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On the modelling of the shallow-water waves with the Coriolis effect
时间  Datetime
2018-12-28 15:00 — 16:00 
地点  Venue
Middle Lecture Room
报告人  Speaker
Yue Liu
单位  Affiliation
Department of Mathematics, University of Texas, Arlington
邀请人  Host
Xiongfeng Yang
报告摘要  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.