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

Abstract

We establish the local well-posedness for the free boundary problem for the compressible Euler equations describing the motion of liquid under the influence of Newtonian self-gravity. We do this by solving a tangentially-smoothed version of Euler's equations in Lagrangian coordinates which satisfies uniform energy estimates as the smoothing parameter goes to zero. The main technical tools are delicate energy estimates and optimal elliptic estimates in terms of boundary regularity, for the Dirichlet problem and Green's function.

arXiv commentCorrected typos

References in corpus (6)

• Well posedness for the motion of a compressible liquid with free surface boundary
• A priori estimates for the free-boundary 3-D compressible Euler equations in physical vacuum
• Well-Posedness for the Motion of Physical Vacuum of the Three-dimensional Compressible Euler Equations with or without Self-Gravitation
• A priori estimates for the motion of a self-gravitating incompressible liquid with free surface boundary
• A priori Estimates for the Compressible Euler Equations for a Liquid with Free Surface Boundary and the Incompressible Limit
• A class of global solutions to the Euler-Poisson system

Cited by in corpus (5)

• Local Well-posedness and Incompressible Limit of the Free-Boundary Problem in Compressible Elastodynamics
• Local Well-posedness for the Motion of a Compressible Gravity Water Wave with Vorticity
• Zero Surface Tension Limit of the Free-Boundary Problem in Incompressible Magnetohydrodynamics
• Local Well-posedness of the Free-Boundary Problem in Compressible Resistive Magnetohydrodynamics
• Anisotropic Regularity of the Free-Boundary Problem in Compressible Ideal Magnetohydrodynamics