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.

arXiv commentTo appear in Journal of Hyperbolic Differential Equations

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• Local well-posedness for the motion of a compressible, self-gravitating liquid with free surface boundary
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