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Quasistatic Motion of a Capillary Drop I. The Two-Dimensional Case

✍ Scribed by Avner Friedman; Fernando Reitich

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
254 KB
Volume
178
Category
Article
ISSN
0022-0396

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✦ Synopsis

A theory is presented for analyzing the nonlinear stability of a drop of incompressible viscous fluid with negligible inertia. The theory is developed here on the twodimensional version of the relevant free-boundary model for Stokes equations. As we show, the two-dimensional problem presents most of the difficulties expected from a projected three-dimensional study while allowing for simpler manipulation of the spherical harmonics. Within this context we show that if the free-boundary initiates close to a circle r=1+el 0 (h), |e| small, then there exists a global-in-time solution with free boundary

which approaches a circle exponentially fast as t Q .. Moreover, we prove that if l 0 (h) is analytic (resp. C . ) in h, then the velocity u(x, t, e), the pressure p(x, t, e), and the free boundary l are all jointly analytic (resp. C .

πŸ“œ SIMILAR VOLUMES

On the Cauchy problem for a capillary dr
On the Cauchy problem for a capillary drop. Part I: irrotational motion
✍ Klaus Beyer; Matthias GΓΌnther πŸ“‚ Article πŸ“… 1998 πŸ› John Wiley and Sons 🌐 English βš– 253 KB

## Communicated by W. Wendland The Cauchy problem for the motion of a liquid drop under surface tension is solved locally in time on the basis of a general abstract existence theorem for Hamiltonian systems which seems to be of interest also in other areas. 1998 B. G. Teubner Stuttgart-John Wiley