A priori estimates for the motion of a self-gravitating incompressible liquid with free surface boundary

Abstract

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.Comment: To appear in Journal of Hyperbolic Differential Equation