In 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.
A PRIORI ESTIMATES FOR THE MOTION OF A SELF-GRAVITATING INCOMPRESSIBLE LIQUID WITH FREE SURFACE BOUNDARY