# Journal article

## 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.

### Access Document

Publisher copy:
10.1007/s00220-010-1028-5

### Authors

More by this author
Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Role:
Author
Journal:
Communications in Mathematical Physics
Volume:
296
Issue:
2
Pages:
559-587
Publication date:
2009-06-01
DOI:
EISSN:
1432-0916
ISSN:
0010-3616
Language:
English
Keywords:
Pubs id:
pubs:404774
UUID:
uuid:ceb7a2b2-7aaf-4cc7-8439-0261d359bf78
Local pid:
pubs:404774
Source identifiers:
404774
Deposit date:
2013-11-16

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