Speaker： Prof. Shengfu Deng

                        Huaqiao University

Title:    Exact Theory of Three-Dimensional Multi-Hump Gravity-Capillary Water Wave

 Time：06 Jan 2020, 15:30

Location：Conference Room 105 at Experiment Building at Haiyun Campus

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.