Large-amplitude solitary water waves with discontinuous vorticity
No Thumbnail Available
Authors
Meeting name
Sponsors
Date
Journal Title
Format
Thesis
Subject
Abstract
Consider a two-dimensional body of water with constant density which lies below a vacuum. The ocean bed is assumed to be impenetrable, while the boundary which separates the uid and the vacuum is assumed to be a free boundary. Under the assumption that the vorticity is only bounded and measurable, we prove that for any upstream velocity field, there exists a continuous curve of large-amplitude solitary wave solutions. This is achieved via a local and global bifurcation construction of weak solutions to the elliptic equations which constitute the steady water wave problem. We also show that such solutions possess a number of qualitative features; most significantly that each solitary wave is a symmetric, monotone wave of elevation.
Table of Contents
PubMed ID
Degree
Ph. D.
Thesis Department
Rights
OpenAccess.
License
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 License.