Local Well-Posedness for the Motion of a Compressible, Self-Gravitating Liquid with Free Surface Boundary

  • Daniel GinsbergEmail author
  • Hans Lindblad
  • Chenyun Luo


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.



The authors would like to thank Jeffrey Marino and Junyan Zhang for reading the first draft of our paper.


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Authors and Affiliations

  1. 1.Program in Applied and Computational MathematicsPrinceton UniversityPrincetonUSA
  2. 2.Department of MathematicsVanderbilt UniversityNashvilleUSA

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