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Home » Water waves and other interface problems (Part 1): Traveling waves with multi-valued height

Seminar

Water waves and other interface problems (Part 1): Traveling waves with multi-valued height April 06, 2021 (08:00 AM PDT - 09:00 AM PDT)
Parent Program:
Location: MSRI: Online/Virtual
Speaker(s) David Ambrose
Description

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

 

Video

Traveling Waves with Multi-Valued Height

Abstract/Media

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

A family of exact pure capillary traveling waves, the Crapper waves, contains waves for which the height of the surface is not a graph with respect to the horizontal (i.e., the height is multi-valued).  Many existence theories for traveling water waves, however, make an explicit assumption that height is single-valued.  While traveling irrotational gravity water waves might not overturn, in more general settings, this assumption of single-valued height is unnecessarily restrictive.  We report progress on two fronts for existence theory for traveling waves with multi-valued height: perturbation results for the Crapper waves which demonstrate that there exist traveling waves with multi-valued height beyond the pure capillary setting, and development and implementation of a formulation for traveling waves which does not restrict to single-valued height and which is suitable for use in both the two-dimensional and three-dimensional settings.

 

Asset no preview Notes 1.41 MB application/pdf

Traveling Waves with Multi-Valued Height