### Abstract

We show that the time decay rate of L^{2} norm of weak solution for the Stokes equations and for the Navier-Stokes equations on the half spaces are t^{-n/2 (1/r - 1/2) - 1/2} if the initial data u_{0} ∈ L^{2}∩L^{r} and ∫_{ℝn+}\y_{n}u_{0}(y)|^{r} dy < ∞ for 1 < r < 2. We also show that the decay rate is determined by the linear part of the weak solution. We use the heat kernel and Ukai's solution formula for the Stokes equations. It has been known up to now that the decay rate on the half space was t^{-n/2 (1/r - 1/2)}, which was obtained by Borchers and Miyakawa [1] and Ukai [9].

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

Pages (from-to) | 799-816 |

Number of pages | 18 |

Journal | Mathematische Zeitschrift |

Volume | 238 |

Issue number | 4 |

DOIs | |

Publication status | Published - 2001 Dec |

### All Science Journal Classification (ASJC) codes

- Mathematics(all)

## Fingerprint Dive into the research topics of 'Decay rate for the incompressible flows in half spaces'. Together they form a unique fingerprint.

## Cite this

Bae, H. O., & Choe, H. J. (2001). Decay rate for the incompressible flows in half spaces.

*Mathematische Zeitschrift*,*238*(4), 799-816. https://doi.org/10.1007/s002090100276