### Abstract

In this paper, we consider the asymptotic behavior of an incompressible fluid around a bounded obstacle. By adapting the Schauder's estimate for stationary Navier–Stokes equation to improve the regularity, the problem is solved by using appropriate Carleman estimates. It should be noted that the minimal decaying rate for a general scalar equation is exp(−C|x|^{2+}). However, the structure of the Navier–Stokes is special. Under the assumption for any nontrivial solution to be uniform bounded which is weaker than those in [10], we got the minimal decaying rate is exp(−C|x|^{[Formula presented]+}) which is better than the results in general scalar cases.

Original language | English |
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Pages (from-to) | 3279-3309 |

Number of pages | 31 |

Journal | Journal of Differential Equations |

Volume | 266 |

Issue number | 6 |

DOIs | |

Publication status | Published - 2019 Mar 5 |

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### All Science Journal Classification (ASJC) codes

- Analysis
- Applied Mathematics

### Cite this

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*Journal of Differential Equations*, vol. 266, no. 6, pp. 3279-3309. https://doi.org/10.1016/j.jde.2018.09.002

**On decay rate of solutions for the stationary Navier–Stokes equation in an exterior domain.** / Kow, Pu Zhao; Lin, Ching-Lung.

Research output: Contribution to journal › Article

TY - JOUR

T1 - On decay rate of solutions for the stationary Navier–Stokes equation in an exterior domain

AU - Kow, Pu Zhao

AU - Lin, Ching-Lung

PY - 2019/3/5

Y1 - 2019/3/5

N2 - In this paper, we consider the asymptotic behavior of an incompressible fluid around a bounded obstacle. By adapting the Schauder's estimate for stationary Navier–Stokes equation to improve the regularity, the problem is solved by using appropriate Carleman estimates. It should be noted that the minimal decaying rate for a general scalar equation is exp(−C|x|2+). However, the structure of the Navier–Stokes is special. Under the assumption for any nontrivial solution to be uniform bounded which is weaker than those in [10], we got the minimal decaying rate is exp(−C|x|[Formula presented]+) which is better than the results in general scalar cases.

AB - In this paper, we consider the asymptotic behavior of an incompressible fluid around a bounded obstacle. By adapting the Schauder's estimate for stationary Navier–Stokes equation to improve the regularity, the problem is solved by using appropriate Carleman estimates. It should be noted that the minimal decaying rate for a general scalar equation is exp(−C|x|2+). However, the structure of the Navier–Stokes is special. Under the assumption for any nontrivial solution to be uniform bounded which is weaker than those in [10], we got the minimal decaying rate is exp(−C|x|[Formula presented]+) which is better than the results in general scalar cases.

UR - http://www.scopus.com/inward/record.url?scp=85052917427&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85052917427&partnerID=8YFLogxK

U2 - 10.1016/j.jde.2018.09.002

DO - 10.1016/j.jde.2018.09.002

M3 - Article

VL - 266

SP - 3279

EP - 3309

JO - Journal of Differential Equations

JF - Journal of Differential Equations

SN - 0022-0396

IS - 6

ER -