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数学学科现代分析及其应用研究所(2020非线性分析与偏微分方程系列报告会二十五)

发布者:数学与计算机科学学院   发布时间:2020-11-18  浏览次数:175

报告题目54Lagrangian Approach to Global Well-Posedness of the Viscous Surface Wave Equations Without Surface Tension

报告人:桂贵龙(西北大学数学学院)

会议时间:2020/11/20 14:00-15:00

腾讯会议ID807 742 031https://meeting.tencent.com/s/KkJmU9YWtrWb

摘要We revisit in this talk the global well-posedness of the classical viscous surface waves in the absence of surface tension effect with the reference domain being the horizontal infinite slab, for which the first complete proof was given in Guo-Tice [Anal PDE 6,1429–1533 (2013)] via a hybrid of Eulerian and Lagrangian schemes. The fluid dynamics are governed by the gravity-driven incompressible Navier-Stokes equations. Even though Lagrangian formulation is most natural to study free boundary value problems for incompressible flows, few mathematical works for global existence are based on such an approach in the absence of surface tension effect, due to breakdown of Beale's transformation. We develop a mathematical approach to establish global well-posedness based on the Lagrangian framework by analyzing suitable good unknowns associated with the problem, which requires no nonlinear compatibility conditions on the initial data.

报告人简介:桂贵龙,西北大学数学学院教授,博士生导师。20107月在中国科学院数学与系统科学研究院数学研究所获理学博士学位;20118-20128月在香港中文大学数学科学研究所从事博士后研究工作。2011年荣获第十届钟家庆数学奖。主要研究流体力学方程组的数学理论。在本领域国际数学杂志Comm. Pure Appl. Math., Adv. Math., Comm. Math. Phys.等发表SCI论文多篇。

 

邀请人:非线性分析与PDE团队