2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/172408In this paper, we prove a priori estimates in Lagrangian coordinates for the equations of motion of an incompressible, inviscid, self-gravitating fluid with free boundary. The estimates show that on a finite time interval we control five derivatives of the fluid velocity and five and a half derivatives of the coordinates of the moving domain.To appear in Journal of Hyperbolic Differential EquationsAnalysis of PDEs76B03text