publication . Article . 1994

On a Model for Narrow-Necked Rotating Liquid Drops

J.E. Ross; D.R. Smith;
Open Access English
  • Published: 01 Mar 1994 Journal: Advances in Applied Mathematics, issue 1, pages 13-96 (issn: 01968858, Copyright policy)
  • Publisher: Academic Press.
AbstractA constructive existence proof is given for a dumbbell-shaped solution near the two-sphere limit for a model of a steadily rigidly rotating liquid drop held together by surface tension. The solution shape is similar to the small solidified glassy dumbbells found in the lunar soil returned by the Apollo 11 Mission. The model problem reduces to a Neumann problem for a nonlinear ordinary differential equation ζ" = F(s, ζ, ζ′) of nonstandard type for which the differential inequality techniques of Nagumo do not apply and for which the resulting linearization does not satisfy standard maximum principles. Our analysis borrows techniques from singular perturbat...
free text keywords: Applied Mathematics, Surface tension, Singular perturbation, Differential equation, Mathematics, Mathematical analysis, Neumann boundary condition, SPHERES, Mathematical model, Linearization, Compressibility
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