Quasi-static motion of a capillary drop, II: the three-dimensional case

[摘要] 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 + epsilonlambda(0)(omega), \epsilon\ small, omega = (theta,phi), then there exists a global-in-time solution with free boundary r = 1 + lambda(omega,t,epsilon) = 1 + Sigma(n greater than or equal to 1)lambda(n)(omega,t)epsilon(n), which approaches a sphere exponentially fast as t --> infinity. Moreover, we prove that if lambda(0)(omega) is analytic (resp. C ') in omega, then the velocity (u) over right arrow (x, t, epsilon), the pressure p(x, t, epsilon) and the free-boundary lambda are all jointly analytic (resp, C ') in (x, e). 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. (C) 2002 Elsevier Science (USA). All rights reserved.

[发布日期] 2002-12-10

[关键词] incompressible viscous fluid;Stokes equation;surface tension;stability;vector spherical harmonics