广州大学数学大讲坛第五期
第四十二讲——德克萨斯大学刘跃教授学术报告
时间：2023年6月12日(周一)上午10：15--11：15
题目：The long wave approximation of the Green-Naghdi equations with the Coriolis effect
地点:理学实验楼314
报告人：刘跃(Yue Liu)教授
摘要：In this talk we study the long wave asymptotic behavior of the rotation- Green-Naghdi equations, which could be used to describe the propagation of long-crested shallow-water waves in the equatorial ocean regions with the Coriolis effect due to Earth's rotation. We demonstrate the lift span of the solution to the R-GN model equations in a Sobolev space by the refined energy estimates. Then we provide a rigorous justification from the solutions of the R-GN equations to the associated solution of the right-left R-BBM or KdV equation in the KdV regime with the small amplitude and the large wavelength. This is the first result on the issue that the solution of the R-GN equations is well approximated by the two directional R-BBM in the general regular initial data setting.
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报告人简介：
刘跃，美国德克萨斯大学阿灵顿分校教授，1994年获布朗大学博士学位，师从国际著名数学家Walter Strauss教授。在偏微分方程，应用分析和流体力学，可积系统与孤子理论，非线性波方程的稳定性理论、奇异性形成、局部和整体适定性等领域取得国际领先的成果。在“Comm. Pure Appl. Math.”、“Adv. Math.”、“Comm. Math. Phys.”、“Arch. Ration.Mech. Anal.”、“J. Funct. Anal.”、“Physica D”、“J. Differential Equations”、“Nonlinearity”、“Quart. of Appl. Math.”等国际著名刊物上发表论文100余篇。
