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

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.

References in corpus (2)

• On the Motion of Vortex Sheets with Surface Tension in the 3D Euler Equations with Vorticity
• Local existence for the free boundary problem for the non-relativistic and relativistic compressible Euler equations with a vacuum boundary condition

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