Discussion of a uniqueness result in "Equilibrium Configurations for a Floating Drop"
DOI:
https://doi.org/10.58997/ejde.2023.32Keywords:
Capillarity, unbounded liquid bridges, uniquenessAbstract
We analyze a uniqueness result presented by Elcrat, Neel, and Siegel [1] for unbounded liquid bridges, and show that the proof they presented is incorrect. We add a hypothesis to their stated theorem and prove that their result holds under this condition. Then we use Chebyshev spectral methods to approximate solutions to certain boundary value problems used to check this hypothesis holds at least on a range of cases.
For more information see https://ejde.math.txstate.edu/Volumes/2023/32/abstr.html
References
David Siegel, Alan Elcrat, Robert Neel; Equilibrium configurations for a floating drop, J. Math. Fluid Mech. 6 (2004), no. 4, 405-429. https://doi.org/10.1007/s00021-004-0119-5
Robert Finn; Review of the article "equilibrium configurations for a floating drop" by alan elcrat, robert neel, and david siegel, Mathematical Reviews MR2101889 (2005j:76017) (2005).
David Siegel; Height estimates for capillary surfaces, Pacific J. Math. , 88 (1980), no. 2, 471-515. https://doi.org/10.2140/pjm.1980.88.471
Lloyd N. Trefethen; Spectral methods in matlab, SIAM (2000) 10, xviii+165. https://doi.org/10.1137/1.9780898719598
Ray Treinen; Spectral methods for capillary surfaces described by bounded generating curves, https://arxiv.org/abs/2205.02931.
Bruce Turkington; Height estimates for exterior problems of capillarity type, Pacific J. Math. 88 (1980), no. 2, 517-540.
ttps://doi.org/10.2140/pjm.1980.88.517
Thomas I. Vogel; Symmetric unbounded liquid bridges, Pacific J. Math. 103 (1982), no. 1, 205-241.
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Copyright (c) 2023 Raymond Treinen
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