报告人：桂贵龙教授（西北大学）
时 间：2019年11月24日下午15：00—15：50
地点：华南数学应用与交叉研究中心学术报告厅111
题目：Lagrangian approach to global well-posedness of the viscous surface wave equations without surface tension}
摘要：
In this talk, we consider the global well-posedness of the viscous surface waves without surface tension with the reference domain being the horizontal infinite slab. The fluid dynamics are governed by the gravity-driven incompressible Navier-Stokes equations, and the effect of surface tension is neglected on the free surface. Even though Lagrangian formulation is natural to study free boundary value problems for incompressible flows, there are few mathematical works for global existence based on such an approach. By using the Lagrangian approach, we prove the global well-posedness of the viscous surface wave problem with small initial perturbation near equilibrium and without any nonlinear compatibility conditions on the initial data, which gives a positive answer to the question about solving the global well-posedness of the viscous surface wave equations in the Lagrangian framework in the paper of Beale (1981, CPAM) under the additional assumption of the low horizontal regularity of initial data. This is a new approach different from the work of Guo-Tice (2013, Analysis and PDE) where the flatting transformation was employed.
个人简介：
桂贵龙，博士，西北大学数学学院数学系主任、教授，博士生导师,从事流体力学方程组的数学理论研究。2010年在中国科学院数学与系统科学研究院获得理学博士学位，香港中文大学博士后；2011年荣获第十届钟家庆数学奖(博士奖)。在国际数学杂志Comm. Pure Appl. Math., Adv. Math., Comm. Math. Phys., Arch. Ration. Mech. Anal., J. Math. Pures Appl.等发表SCI学术论文多余篇。主持国家自然科学基金项目2项。