### Abstract

Stability of planar stationary solutions to the compressible Navier-Stokes equation on the half space ℝ_{+}
^{n} (n ≥ 2)$$ under outflow boundary condition is investigated. It is shown that the planar stationary solution is stable with respect to small perturbations in H^{s} (ℝ_{+}
^{n}) s ≥ [n/2]+1 and the perturbations decay in L ^{∞} norm as t →∞, provided that the magnitude of the stationary solution is sufficiently small. The stability result is proved by the energy method. In the proof an energy functional based on the total energy of the system plays an important role.

Original language | English |
---|---|

Pages (from-to) | 401-430 |

Number of pages | 30 |

Journal | Communications in Mathematical Physics |

Volume | 266 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2006 Sep 1 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)
- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

**Stability of planar stationary solutions to the compressible Navier-Stokes equation on the half space.** / Kagei, Yoshiyuki; Kawashima, Shuichi.

Research output: Contribution to journal › Article

*Communications in Mathematical Physics*, vol. 266, no. 2, pp. 401-430. https://doi.org/10.1007/s00220-006-0017-1

}

TY - JOUR

T1 - Stability of planar stationary solutions to the compressible Navier-Stokes equation on the half space

AU - Kagei, Yoshiyuki

AU - Kawashima, Shuichi

PY - 2006/9/1

Y1 - 2006/9/1

N2 - Stability of planar stationary solutions to the compressible Navier-Stokes equation on the half space ℝ+ n (n ≥ 2)$$ under outflow boundary condition is investigated. It is shown that the planar stationary solution is stable with respect to small perturbations in Hs (ℝ+ n) s ≥ [n/2]+1 and the perturbations decay in L ∞ norm as t →∞, provided that the magnitude of the stationary solution is sufficiently small. The stability result is proved by the energy method. In the proof an energy functional based on the total energy of the system plays an important role.

AB - Stability of planar stationary solutions to the compressible Navier-Stokes equation on the half space ℝ+ n (n ≥ 2)$$ under outflow boundary condition is investigated. It is shown that the planar stationary solution is stable with respect to small perturbations in Hs (ℝ+ n) s ≥ [n/2]+1 and the perturbations decay in L ∞ norm as t →∞, provided that the magnitude of the stationary solution is sufficiently small. The stability result is proved by the energy method. In the proof an energy functional based on the total energy of the system plays an important role.

UR - http://www.scopus.com/inward/record.url?scp=33746214642&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33746214642&partnerID=8YFLogxK

U2 - 10.1007/s00220-006-0017-1

DO - 10.1007/s00220-006-0017-1

M3 - Article

AN - SCOPUS:33746214642

VL - 266

SP - 401

EP - 430

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

IS - 2

ER -