Water waves with compactly supported vorticity: A functional-analytic approach to bifurcation theory and the mathematical theory of traveling water waves
We study the mathematical theory of water waves. Local bifurcation theory is also discussed, including the Crandall-Rabinowitz theorem; an abstract theorem used to establish the presence of bifurcation points in the zero set of maps on Banach spaces. A functional-analytic approach is used to prove the existence of a family of localized traveling waves with one or more point vortices, by bifurcating from a trivial solution. This is done in the setting of the incompressible Euler equations with gravity and surface tension, on finite depth. Our result is an extension of a recent result by Shatah, Walsh and Zeng, where existence was shown for a single point vortex on infinite depth. The properties of the resulting waves are also examined: We find that the properties depend significantly on the position of the point vortices in the water column.
Place, publisher, year, edition, pages
Institutt for matematiske fag , 2014. , 114 p.
IdentifiersURN: urn:nbn:no:ntnu:diva-25748Local ID: ntnudaim:11758OAI: oai:DiVA.org:ntnu-25748DiVA: diva2:740209
Ehrnstrøm, Mats, Førsteamanuensis