Work

Axisymmetric capillary water waves with vorticity and swirl connecting to static unduloid configurations

Year: 2024

Type: article

Abstract: We study steady axisymmetric water waves with general vorticity and swirl, subject to the influence of surface tension. Explicit solutions to such a water wave problem are static configurations where the surface is an unduloid, that is, a periodic surface of revolution with constant mean curvature. We prove that to any such configuration there connects a global continuum of non-static solutions by means of a global implicit function theorem. To prove this, the key is strict monotonicity of a certain function describing the mean curvature of an unduloid and involving complete elliptic integrals. From this point of view, this paper is an interesting interplay between water waves, geometry, and properties of elliptic integrals.

Source: Journal of Differential Equations

DOI: 10.1016/j.jde.2024.08.005

Authors: Anna-Mariya Otsetova, Erik Wahlén, Jörg Weber

Institutions: Aalto University, Lund University, University of Vienna

Language: English

Topic: Geometric Analysis and Curvature Flows

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,050

Funder: Vetenskapsrådet