报告题目：The long wave approximation of the Green-Naghdi equations with the Coriolis effect

报告人：Liu Yue，美国德克萨斯大学阿灵顿分校

报告时间：2023年6月28日15:00-16:00

报告地点：20-306

报告摘要：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.

报告人简介：Liu Yue，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。从事非线性偏微分方程数学理论的研究工作。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 App.Math.、Adv.Math.、Comm.Math.Phvs.、Arch.Ration.Mech.Anal.、J.Funct.Anal.、J.Differential Equations、Nonlinearity 等国际著名刊物上发表论文 100 余篇。

邀请人：非线性分析与PDE团队