Speaker： Prof. Shengfu Deng
Title: Exact Theory of Three-Dimensional Multi-Hump Gravity-Capillary Water Wave
Time：06 Jan 2020, 15:30
Abstract: The talk considers three-dimensional traveling surface waves on water of finite depth under the forces of gravity surface tension using the exact governing equations, called Euler equations. It has been shown that when two non-dimensional constants $b$ $\lambda$, which are related to the surface tension wave speed, respectively, near a critical curve in $(b, \lambda )$-plane, the Euler equations have a three-dimensional solution that has a one-hump at center approaching to nonzero oscillations at infinity in the propagation direction is periodic in the transverse direction. Here, it is proved that in this case, the Euler equations have a three-dimensional two-hump solutions with similar properties. These two humps in the propagation direction are far apart connected by small oscillations in the middle. This is the first rigorous study on three-dimensional multi-hump water waves. The essential part of proof is to find appropriate free constants so that two one-hump solutions can be glued together in the middle to form a two-hump solution.
Speaker Introduction：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。