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A Study of Rotational Water Waves using Bifurcation Theory
Norwegian University of Science and Technology, Faculty of Natural Sciences and Technology, Department of Physics.
2014 (English)MasteroppgaveStudent thesis
Abstract [en]

This thesis is concerned with the water wave problem. Using local bifurcation we establish small-amplitude steady and periodic solutions of the Euler equations with vorticity. Our approach is based on that of Ehrnström, Escher and Wahlén \cite{EEW11}, the main difference being that we use new bifurcation parameters. The bifurcation is done both from a one-dimensional and a two-dimensional kernel, the latter bifurcation giving rise to waves having more than one crest in each minimal period. We also give a novel and rudimentary proof of a key lemma establishing the Fredholm property of the elliptic operator associated with the water wave problem. Furthermore, we investigate derivatives of the bifurcation curve, and present a new result for the corresponding linear problem.

Place, publisher, year, edition, pages
Institutt for matematiske fag , 2014. , 73 p.
URN: urn:nbn:no:ntnu:diva-27092Local ID: ntnudaim:11307OAI: diva2:757582
Available from: 2014-10-22 Created: 2014-10-22 Last updated: 2014-10-22Bibliographically approved

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