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## A priori estimates for the free-boundary 3-D compressible Euler equations in physical
vacuum

## Published Web Location

https://arxiv.org/pdf/0906.0289.pdfNo data is associated with this publication.

## Abstract

We prove a priori estimates for the three-dimensional compressible Euler equations with moving {\it physical} vacuum boundary, with an equation of state given by $p(\rho) = C_\gamma \rho^\gamma $ for $\gamma >1$. The vacuum condition necessitates the vanishing of the pressure, and hence density, on the dynamic boundary, which creates a degenerate and characteristic hyperbolic {\it free-boundary} system to which standard methods of symmetrizable hyperbolic equations cannot be applied.