### Abstract

The Navier-Stokes equation for compressible viscous fluid is considered on the half space in R^{3} under the zero-Dirichlet boundary condition for the momentum with initial data near an arbitrarily given equilibrium of positive constant density and zero momentum. Time decay properties in L^{2} norms for solutions of the linearized problem are investigated to obtain the rate of convergence in L^{2} norms of solutions to the equilibrium when initial data are sufficiently close to the equilibrium in H^{3} ∩ L^{1}. Some lower bounds are derived for solutions to the linearized problem, one of which indicates a nonlinear phenomenon not appearing in the case of the Cauchy problem on the whole space.

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

Pages (from-to) | 89-159 |

Number of pages | 71 |

Journal | Archive for Rational Mechanics and Analysis |

Volume | 165 |

Issue number | 2 |

DOIs | |

Publication status | Published - Nov 1 2002 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Analysis
- Mathematics (miscellaneous)
- Mechanical Engineering

### Cite this

^{3}.

*Archive for Rational Mechanics and Analysis*,

*165*(2), 89-159. https://doi.org/10.1007/s00205-002-0221-x

**On large-time behavior of solutions to the compressible Navier-Stokes equations in the half space in R ^{3}.** / Kagei, Yoshiyuki; Kobayashi, Takayuki.

Research output: Contribution to journal › Article

^{3}',

*Archive for Rational Mechanics and Analysis*, vol. 165, no. 2, pp. 89-159. https://doi.org/10.1007/s00205-002-0221-x

^{3}. Archive for Rational Mechanics and Analysis. 2002 Nov 1;165(2):89-159. https://doi.org/10.1007/s00205-002-0221-x

}

TY - JOUR

T1 - On large-time behavior of solutions to the compressible Navier-Stokes equations in the half space in R3

AU - Kagei, Yoshiyuki

AU - Kobayashi, Takayuki

PY - 2002/11/1

Y1 - 2002/11/1

N2 - The Navier-Stokes equation for compressible viscous fluid is considered on the half space in R3 under the zero-Dirichlet boundary condition for the momentum with initial data near an arbitrarily given equilibrium of positive constant density and zero momentum. Time decay properties in L2 norms for solutions of the linearized problem are investigated to obtain the rate of convergence in L2 norms of solutions to the equilibrium when initial data are sufficiently close to the equilibrium in H3 ∩ L1. Some lower bounds are derived for solutions to the linearized problem, one of which indicates a nonlinear phenomenon not appearing in the case of the Cauchy problem on the whole space.

AB - The Navier-Stokes equation for compressible viscous fluid is considered on the half space in R3 under the zero-Dirichlet boundary condition for the momentum with initial data near an arbitrarily given equilibrium of positive constant density and zero momentum. Time decay properties in L2 norms for solutions of the linearized problem are investigated to obtain the rate of convergence in L2 norms of solutions to the equilibrium when initial data are sufficiently close to the equilibrium in H3 ∩ L1. Some lower bounds are derived for solutions to the linearized problem, one of which indicates a nonlinear phenomenon not appearing in the case of the Cauchy problem on the whole space.

UR - http://www.scopus.com/inward/record.url?scp=0036877029&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0036877029&partnerID=8YFLogxK

U2 - 10.1007/s00205-002-0221-x

DO - 10.1007/s00205-002-0221-x

M3 - Article

AN - SCOPUS:0036877029

VL - 165

SP - 89

EP - 159

JO - Archive for Rational Mechanics and Analysis

JF - Archive for Rational Mechanics and Analysis

SN - 0003-9527

IS - 2

ER -