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+

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

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)

Access to Document

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

Fingerprint Dive into the research topics of 'The incompressible limit and the initial layer of the compressible Euler equation in ℝ<sup>n</sup>+'. Together they form a unique fingerprint.

Cite this

@article{7e4c272754b041d489e6b4b7d6551d27,

title = "The incompressible limit and the initial layer of the compressible Euler equation in ℝn+",

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.",

author = "Tatsuo Iguchi",

year = "1997",

month = jul,

day = "25",

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

language = "English",

volume = "20",

pages = "945--958",

journal = "Mathematical Methods in the Applied Sciences",

issn = "0170-4214",

publisher = "John Wiley and Sons Ltd",

number = "11",

}

TY - JOUR

T1 - The incompressible limit and the initial layer of the compressible Euler equation in ℝn+

AU - Iguchi, Tatsuo

PY - 1997/7/25

Y1 - 1997/7/25

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.

UR - http://www.scopus.com/inward/record.url?scp=4143051326&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=4143051326&partnerID=8YFLogxK

U2 - 10.1002/(SICI)1099-1476(19970725)20:11<945::AID-MMA894>3.0.CO;2-T

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

M3 - Article

AN - SCOPUS:4143051326

VL - 20

SP - 945

EP - 958

JO - Mathematical Methods in the Applied Sciences

JF - Mathematical Methods in the Applied Sciences

SN - 0170-4214

IS - 11

ER -