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doi:10.1016/S0022-0396(02)00034-7 
Copyright © 2002 Elsevier Science (USA). All rights reserved.
Quasi-static motion of a capillary drop, II: the three-dimensional case
Received 8 August 2001;
revised 26 February 2002;
accepted 16 April 2002. ;
Available online 26 November 2002.
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Abstract
A theory is presented to analyze the nonlinear stability of a drop of incompressible viscous fluid with negligible inertia. The theory is developed here on the three-dimensional version of the relevant free-boundary model for Stokes equations. Within this context we show that if the free-boundary initiates close to a sphere
r=1+
λ0(ω), || small, ω=(θ,
),
λ0(ω), || small, ω=(θ,),) and the free-boundary λ are all jointly analytic (resp. C∞) in (x,). In an earlier paper, we considered the analogous problem for a two-dimensional drop. Although the three-dimensional problem proceeds along similar lines, the analysis is more complicated due to the fact that we work here with spherical harmonics and vector spherical harmonics. Author Keywords: Incompressible viscous fluid; Stokes equation; Surface tension; Stability; Vector spherical harmonics
Mathematical subject codes: primary 35R35; 76D07; 76D45; secondary 35J55
Article Outline
- 1. The problem
- 2. Vector spherical harmonics
- 3. Reduction of ((1.12) and (1.13)) to ODEs
- 4. Reduction of ((1.14) and (1.15))
- 5. Reduction to Ωδ(t)
- 6. Redundancy
- 7. Reduction to {δ<r<1}
- 8. Reduction to {δ<r<1} (continued)
- 9. The ODE system
- 10. Solution of the ODE system
- 11. A fundamental lemma
- 12. Convergence
- Acknowledgements
- References
