2018年01月23日 |  English version
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Asymptotic analysis on the modelling of the shallow-water waves with the Coriolis effect

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,德克萨斯大学阿灵顿分校
报告时间:2018年1月5日(周五)下午3:00
报告地点:行健楼学术活动室526
邀 请 人:田立新 教授
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.

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