The incompressible limit and the initial layer of the compressible Euler equation in ℝn+

Tatsuo Iguchi

doi:10.1002/(SICI)1099-1476(19970725)20:11<945::AID-MMA894>3.0.CO;2-T

The incompressible limit and the initial layer of the compressible Euler equation in ℝⁿ+

Tatsuo Iguchi

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

We consider the incompressible limit of the compressible Euler equation in the half-space ℝⁿ₊. 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 data v∞₀ do not satisfy the condition '∇·v∞₀ = 0', then the initial layer will appear.

Original language	English
Pages (from-to)	945-958
Number of pages	14
Journal	Mathematical Methods in the Applied Sciences
Volume	20
Issue number	11
DOIs	https://doi.org/10.1002/(SICI)1099-1476(19970725)20:11<945::AID-MMA894>3.0.CO;2-T
Publication status	Published - 1997 Jul 25
Externally published	Yes

ASJC Scopus subject areas

Mathematics(all)
Engineering(all)

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10.1002/(SICI)1099-1476(19970725)20:11<945::AID-MMA894>3.0.CO;2-T

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abstract = "We consider the incompressible limit of the compressible Euler equation in the half-space ℝn+. 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 data v∞0 do not satisfy the condition '∇·v∞0 = 0', then the initial layer will appear.",

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N2 - We consider the incompressible limit of the compressible Euler equation in the half-space ℝn+. 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 data v∞0 do not satisfy the condition '∇·v∞0 = 0', then the initial layer will appear.

AB - We consider the incompressible limit of the compressible Euler equation in the half-space ℝn+. 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 data v∞0 do not satisfy the condition '∇·v∞0 = 0', then the initial layer will appear.

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The incompressible limit and the initial layer of the compressible Euler equation in ℝⁿ+

Abstract

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