Well-posedness for compressible Euler equations with physical vacuum singularity
نویسندگان
چکیده
منابع مشابه
Well-posedness for compressible Euler equations with physical vacuum singularity
An important problem in the theory of compressible gas flows is to understand the singular behavior of vacuum states. The main difficulty lies in the fact that the system becomes degenerate at the vacuum boundary, where the characteristics coincide and have unbounded derivative. In this paper, we overcome this difficulty by presenting a new formulation and new energy spaces. We establish the lo...
متن کاملWell-posedness for compressible Euler with physical vacuum singularity
An important problem in the theory of compressible gas flows is to understand the singular behavior of vacuum states. The main difficulty lies in the fact that the system becomes degenerate at the vacuum boundary, where the characteristics coincide and have unbounded derivative. In this paper, we overcome this difficulty by presenting a new formulation and new energy spaces. We establish the lo...
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An important problem in gas and fluid dynamics is to understand the behavior of vacuum states, namely the behavior of the system in the presence of vacuum. In particular, physical vacuum, in which the boundary moves with a nontrivial finite normal acceleration, naturally arises in the study of the motion of gaseous stars or shallow water. Despite its importance, there are only few mathematical ...
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The free-boundary compressible one-dimensional Euler equations with moving physical vacuum boundary are a system of hyperbolic conservation laws that are both characteristic and degenerate. The physical vacuum singularity (or rate of degeneracy) requires the sound speed c2 D 1 to scale as the square root of the distance to the vacuum boundary and has attracted a great deal of attention in recen...
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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 = γργ−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...
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ژورنال
عنوان ژورنال: Communications on Pure and Applied Mathematics
سال: 2009
ISSN: 0010-3640,1097-0312
DOI: 10.1002/cpa.20285