Resumen
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 two-dimensional 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 then there exists a global-in-time solution with free boundary which approaches a circle exponentially fast as t. Moreover, we prove that if 0() is analytic (resp. C) in , then the velocity u (x, t, ), the pressure p (x, t, ), and the free boundary are all jointly analytic (resp. C) in (x, ).