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Well-posedness in smooth function spaces for the moving-boundary 1-D compressible Euler equations in physical vacuum

Abstract:

The free-boundary compressible 1-D Euler equations with moving physical vacuum boundary are a system of hyperbolic conservation laws which are both characteristic and degenerate. The physical vacuum singularity (or rate-of-degeneracy) requires the sound speed $c= \gamma \rho^{\gamma -1}$ to scale as the square-root of the distance to the vacuum boundary, and has attracted a great deal of attention in recent years. We establish the existence of unique solutions to this system on a short time-i...

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Publisher copy:
10.1002/cpa.20344

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Institution:
University of Oxford
Department:
Oxford, MPLS, Mathematical Inst
Role:
Author
Journal:
Communications on Pure and Applied Mathematics
Volume:
64
Issue:
3
Pages:
328-366
Publication date:
2009-10-16
DOI:
EISSN:
0010-3640
ISSN:
0010-3640
URN:
uuid:1a52058d-56cc-43bf-8f16-cd6a9699f92b
Source identifiers:
404770
Local pid:
pubs:404770

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