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Mathematics > Analysis of PDEs

arXiv:2202.01754 (math)
[Submitted on 3 Feb 2022 (v1), last revised 8 Mar 2022 (this version, v2)]

Title:Bifurcation analysis for axisymmetric capillary water waves with vorticity and swirl

Authors:André Erhardt, Erik Wahlén, Jörg Weber
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Abstract:We study steady axisymmetric water waves with general vorticity and swirl, subject to the influence of surface tension. This can be formulated as an elliptic free boundary problem in terms of Stokes' stream function. A change of variables allows us to overcome the generic coordinate-induced singularities and to cast the problem in the form "identity plus compact", which is amenable to Rabinowitz' global bifurcation theorem, while no restrictions regarding the absence of stagnation points in the flow have to be made. Within the scope of this new formulation, local and global solution curves, bifurcating from laminar flows with a flat surface, are constructed.
Subjects: Analysis of PDEs (math.AP)
MSC classes: 35B07, 35B32, 76B15, 76B45, 76B47
Cite as: arXiv:2202.01754 [math.AP]
  (or arXiv:2202.01754v2 [math.AP] for this version)
  https://doi.org/10.48550/arXiv.2202.01754
Journal reference: Stud. Appl. Math. 149 (2022), no. 4, 904-942
Related DOI: https://doi.org/10.1111/sapm.12525

Submission history

From: Jörg Weber [view email]
[v1] Thu, 3 Feb 2022 18:21:03 UTC (202 KB)
[v2] Tue, 8 Mar 2022 08:35:16 UTC (203 KB)
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