A priori estimates for the free-boundary 3-D compressible Euler equations in physical vacuum
Open Access Publications from the University of California

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

• Author(s): Coutand, Daniel
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.