Abstract:
We consider an incompressible fluid contained in a toroidal stratum which is only subjected to Newtonian self-attraction. Under the assumption of infinitesimal thickness of the stratum we show the existence of stationary motions during which the stratum is approximately a round torus (with radii r, R and R≫r) that rotates around its axis and at the same time rolls on itself. Therefore each particle of the stratum describes an helix-like trajectory around the circumference of radius R that connects the centers of the cross sections of the torus.
\Bibitem{FusNegOli12}
\by Giorgio Fusco, Piero Negrini, Waldyr M. Oliva
\paper Stationary Motion of a Self-gravitating Toroidal Incompressible Liquid Layer
\jour Regul. Chaotic Dyn.
\yr 2012
\vol 17
\issue 5
\pages 397--416
\mathnet{http://mi.mathnet.ru/rcd411}
\crossref{https://doi.org/10.1134/S1560354712050036}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2989513}
\zmath{https://zbmath.org/?q=an:1333.37116}
\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?2012RCD....17..397F}
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https://www.mathnet.ru/eng/rcd411
https://www.mathnet.ru/eng/rcd/v17/i5/p397
This publication is cited in the following 1 articles:
Waldyr Oliva, “Opening note on the occasion of the 8th IST-IME Meeting, September 5–9, 2022, Instituto Superior Técnico, Lisbon, Portugal, on Ordinary and Partial Differential Equations and Related Topics”, São Paulo J. Math. Sci., 2024
Citation in format AMSBIB
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