报告名称：Global well-posedness of the viscous surface wave problem

报告专家：王焰金

专家所在单位：厦门大学

报告时间：2021年11月26日：14：00-18：00

报告地点：腾讯会议

专家简介：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美国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等。曾获全国优秀博士学位论文奖，入选国家高层次青年人才。

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. By exploiting the anisotropic decay rates of the velocity, which are even not integrable, we prove the global well-posedness in both 2D and 3D, without any low frequency assumption of the initial data. One of key observations here is a cancellation in nonlinear estimates of the viscous stress tensor term in the bulk by using Alinhac good unknowns, when estimating the energy evolution of the highest order horizontal spatial derivatives of the solution.

邀请人：向妮

（审核：郑大彬）