應yl7703永利官網(wǎng)王智誠教授和張亮教授的邀請，華僑大學鄧圣福教授將于2023年9月25日-26日訪問蘭州大學，期間于9月26日舉辦線上專題學術報告。
報告題目：The Existence of Three-Dimensional Multi-Hump Gravity-Capillary Surface Waves on Water of Finite Depth
時 間：9月26日下午19:00.
地 點：騰訊會議66717204004
報告摘要：This talk considers three-dimensional traveling surface waves on water of finite depth under the forces of gravity and surface tension using the exact governing equations, also called Euler equations. It was known that when two non-dimensional constants $b$ and $\lambda$, which are related to the surface-tension coefficient and the traveling wave speed, respectively, near a critical curve in the $(b, \lambda)$-plane, the Euler equations have a three-dimensional (3D) solution that has one hump at the center, approaches nonzero oscillations at infinity in the propagation direction, and is periodic in the transverse direction. We prove that in this parameter region, the Euler equations also have a 3D two-hump solution with similar properties. These two humps in the propagation direction are far apart and connected bysmall oscillations in the middle. The result obtained here is the first rigorous proof on the existence of 3D multi-hump water waves. The main idea of the proof is to find appropriate free constants and derive the necessary estimates of the solutions for the Euler equations in terms of those free constants so that two 3D one-hump solutions that are far apart can be successfully matched in the middle to form a 3D two-hump solution if some values of those constants are specified from matching conditions. The idea may also be applied to study the existence of 3D $2^n$-hump water-waves.
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報告人簡介：
鄧圣福，華僑大學教授，福建省“閩江學者獎勵計劃”特聘教授，從事微分方程與動力系統(tǒng)理論及其在水波問題上的應用。先后主持國家自然科學面上基金3項、教育部留學回國人員科研啟動基金、中國博士后科學基金、福建省自然科學基金、廣東省自然科學基金、廣東省“揚帆計劃”引進緊缺拔尖人才項目等，并入選廣東省高等學?！扒О偈瞬排囵B(yǎng)工程”省級培養(yǎng)對象。在Arch. Rational Mech. Anal.、SIAM J. Math. Anal.、Nonlinearity、J. Differential Equations、Physica D等國際重要學術期刊上發(fā)表論文40多篇。
甘肅應用數(shù)學中心
甘肅省高校應用數(shù)學與復雜系統(tǒng)省級重點實驗室
yl7703永利官網(wǎng)
萃英學院
2023年9月24日
