### Abstract

Consider the nonstationary Stokes equations in exterior domains Ω ⊂ ℝ^{n} (n ≥ 3) with the compact boundary ∂Ω. We show first that the solution u(t) decays like ∥u(t)∥_{r} = O(t^{-n/2(1-1/r})) for all 1 < r ≤ ∞ as t → ∞. This decay rate n/2(1 - 1/r) is optimal in the sense that ∥u(t)∥_{r} = o(t^{-n/2(1-1/r})) for some 1 < r ≤ ∞ as t → ∞ occurs if and only if the net force exerted by the fluid on ∂Ω is zero.

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

Pages (from-to) | 709-730 |

Number of pages | 22 |

Journal | Mathematische Annalen |

Volume | 320 |

Issue number | 4 |

DOIs | |

Publication status | Published - 2001 |

Externally published | Yes |

### Fingerprint

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

**Rapid time-decay and net force to the obstacles by the Stokes flow in exterior domains.** / Kozono, Hideo.

Research output: Contribution to journal › Article

*Mathematische Annalen*, vol. 320, no. 4, pp. 709-730. https://doi.org/10.1007/s002080100214

}

TY - JOUR

T1 - Rapid time-decay and net force to the obstacles by the Stokes flow in exterior domains

AU - Kozono, Hideo

PY - 2001

Y1 - 2001

N2 - Consider the nonstationary Stokes equations in exterior domains Ω ⊂ ℝn (n ≥ 3) with the compact boundary ∂Ω. We show first that the solution u(t) decays like ∥u(t)∥r = O(t-n/2(1-1/r)) for all 1 < r ≤ ∞ as t → ∞. This decay rate n/2(1 - 1/r) is optimal in the sense that ∥u(t)∥r = o(t-n/2(1-1/r)) for some 1 < r ≤ ∞ as t → ∞ occurs if and only if the net force exerted by the fluid on ∂Ω is zero.

AB - Consider the nonstationary Stokes equations in exterior domains Ω ⊂ ℝn (n ≥ 3) with the compact boundary ∂Ω. We show first that the solution u(t) decays like ∥u(t)∥r = O(t-n/2(1-1/r)) for all 1 < r ≤ ∞ as t → ∞. This decay rate n/2(1 - 1/r) is optimal in the sense that ∥u(t)∥r = o(t-n/2(1-1/r)) for some 1 < r ≤ ∞ as t → ∞ occurs if and only if the net force exerted by the fluid on ∂Ω is zero.

UR - http://www.scopus.com/inward/record.url?scp=0035596593&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0035596593&partnerID=8YFLogxK

U2 - 10.1007/s002080100214

DO - 10.1007/s002080100214

M3 - Article

AN - SCOPUS:0035596593

VL - 320

SP - 709

EP - 730

JO - Mathematische Annalen

JF - Mathematische Annalen

SN - 0025-5831

IS - 4

ER -