[PAST EVENT] Mathematics Colloquium: Shu-Ming Sun (Virginia Polytechnic Institute and State University)
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Mathematics Colloquium: Shu-Ming Sun (Virginia Polytechnic Institute and State University)
Title: Exact theory on solitary or multi-solitary water waves
Abstract: The talk will discuss recent development on the existence of two- and three-dimensional solitary or multi-solitary surface waves on the water of finite depth with or without suface tension using the exact governing equations (called Euler equations). It will be shown that when the nondimensional wave-speed and surface tension are in various regions, the Euler equations possess several different kinds of two- or three-dimensional solitary or multi-solitary wave solutions. Moreover, some stability results for these waves will be addressed, such as transverse instability, spectral stability, asymptotic linear stability or conditional stability. The talk is accessible to non-experts or graduate students.