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Exact Two-Dimensional Multi-Hump Waves on Water of Finite Depth with Small Surface Tension
邓圣福 教授(华侨大学)
2019-5-16 下午 15:20?16:05  闵行数学楼126室

报告人简介:邓圣福, 华侨大学特聘教授,“闽江学者奖励计划”特聘教授,从事微分方程与动力系统理论及其在水波问题上的应用。先后主持国家自然科学面上基金2项、教育部留学回国人员科研启动基金、中国博士后科学基金、广东省自然科学基金、广东省“扬帆计划”引进紧缺拔尖人才项目等,并入选广东省高等学校“千百十人才培养工程”省级培养对象。在SIAM J. Math. Anal.、Nonlinearity、J. Differential Equations、Physica D、Discr. Contin. Dynam. Systems A、IMA J. Appl. Math.等国际重要学术期刊上发表论文30多篇。

报告内容简介: The talk concerns the existence of multi-hump traveling waves propagating on the free surface of a two-dimensional water channel under the influence of gravity and small surface tension force. The fluid of constant density is assumed to be inviscid and incompressible and the flow is irrotational. It has been known that the exact governing equations, called Euler equations, possess a generalized solitary-wave solution of elevation that consists of a single crest (or hump) at the center and a much smaller oscillation at infinity. This paper provides the first proof of the existence of multi-hump waves using the Euler equations. It is shown that when the wave speed is near its critical value and surface tension is small, the Euler equations have a two-hump solution which consists of two crests, that are spaced far apart, and a smaller oscillation at infinity. Moreover, the ideas and methods may be used to study $2^m$-hump solutions.

主持人: 刘兴波教授
主办单位:数学科学学院 科技处