报告人：王焰金（厦门大学）

邀请人：雷远杰

报告时间：2021年1月19日（星期二）10:00-12:00

报告地点：腾讯会议ID：457 726 612

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

报告摘要：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，国家高层次青年人才、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。