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学术讲座 Lecture

【21.1.8 10:30-11:30】学术报告---王焰金教授

2021-01-07 09:06:16 来源:学术报告---王焰金教授 点击: 收藏本文

报告人:王焰金教授(厦门大学)

时 间:2021年1月8日上午 10:30-11:30

地点:华南数学应用与交叉研究中心学术报告厅111

题目:Global well-posedness of the viscous surface wave problem


摘要:

Consider a viscous incompressible fluid below the air and above a fixed bottom. The fluid dynamics is governed by the gravity-driven incompressible Navier-Stokes equations, and the effect of surface tension is neglected on the free surface. The global well-posedness and long-time behavior of solutions near equilibrium have been intriguing questions since Beale (1981). It was proved by Guo and Tice (2013) that with certain additional low horizontal frequency assumption of the initial data in 3D an integrable decay rate of the velocity is obtained so that the global unique solution can be constructed, while the global well-posedness in 2D was left open. We prove the global well-posedness in both 2D and 3D, without any low frequency assumption of the initial data. The key ingredients are a nonlinear cancellation by using Alinhac good unknowns and the improved anisotropic decay rates of the velocity, which are even not integrable.


报告人简介:

王焰金,博士,厦门大学数学科学学院教授、博士生导师。2005年本科和2011年博士毕业于厦门大学,2009.9-2010.12布朗大学联合培养博士,2013.9-2014.9香港中文大学博士后。主要从事流体力学中的非线性偏微分方程的数学理论研究,论文发表在Adv. Math.、ARMA、CMP、CPDE、JMPA、SIMA等。