Exact theory on existence and stability of solitary water waves
Professor Shu-Ming SunDepartment of Math., Virginia Tech. USA 下午 3:00–5:00 鴻經館 107 室Abstract:
The talk will discuss most recent development on the existence and stability of two- and three-dimensional solitary waves on the surface of water of finite depth with or without surface tension using the exact governing equations. It is well-known that the motion of surface waves of this problem is determined by two non-dimensional constants: non-dimensional wave speed F and surface tension B. It will be shown that the exact governing equations have many different kinds of two- and three-dimensional waves when (F, B) is in different parameter regions. Moreover, various stability results for these waves will be addressed, such as transverse stability, spectral stability, asymptotic linear stability or conditional stability.