### Abstract

We consider the incompressible limit of the compressible Euler equation in the half-space ℝ^{n}_{+}. 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 |

Publication status | Published - 1997 Jul 25 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

**The incompressible limit and the initial layer of the compressible Euler equation in ℝ ^{n}+.** / Iguchi, Tatsuo.

Research output: Contribution to journal › Article

^{n}+',

*Mathematical Methods in the Applied Sciences*, vol. 20, no. 11, pp. 945-958.

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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

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 -