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A note on incompressible limit for compressible Euler equations

โœ Scribed by Jiang Xu; Wen-An Yong

Publisher
John Wiley and Sons
Year
2011
Tongue
English
Weight
147 KB
Volume
34
Category
Article
ISSN
0170-4214

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โœฆ Synopsis

This paper presents a simple justification of the classical low Mach number limit in critical Besov spaces for compressible Euler equations with prepared initial data. As the first step of this justification, we formulate a continuation principle for general hyperbolic singular limit problems in the framework of critical Besov spaces. With this principle, it is also shown that, for the Mach number sufficiently small, the smooth compressible flows exist on the (finite) time interval where the incompressible Euler equations have smooth solutions, and the definite convergence orders are obtained.

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โœ Tatsuo Iguchi ๐Ÿ“‚ Article ๐Ÿ“… 1997 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 329 KB ๐Ÿ‘ 2 views

We consider the incompressible limit of the compressible Euler equation in the half-space 1L > . It is proved that the solutions of the non-dimensionalized compressible Euler equation converge to the solution of the incompressible Euler equation when the Mach number tends to zero. If the initial dat