### 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 |
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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 |

### All Science Journal Classification (ASJC) codes

- Analysis
- Mathematics (miscellaneous)
- Mechanical Engineering

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## Cite this

^{3}.

*Archive for Rational Mechanics and Analysis*,

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