### Abstract

We show existence theorem of global mild solutions with small initial data and external forces in the time-weighted Besov space which is an invariant space under the change of scaling. The result on local existence of solutions for large data is also discussed. Our method is based on the Lp-Lq estimate of the Stokes equations in Besov spaces. Since we construct the global solution by means of the implicit function theorem, as a byproduct, its stability with respect to the given data is necessarily obtained.

Original language | English |
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Journal | Mathematische Nachrichten |

DOIs | |

Publication status | Accepted/In press - 2018 Jan 1 |

### Fingerprint

### Keywords

- 35Q30
- 76D03
- 76D05
- Global well-posedness
- Navier-Stokes equations
- Singular data
- Time-weighted Besov spaces

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Mathematische Nachrichten*. https://doi.org/10.1002/mana.201700078

**Navier-Stokes equations with external forces in time-weighted Besov spaces.** / Kozono, Hideo; Shimizu, Senjo.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Navier-Stokes equations with external forces in time-weighted Besov spaces

AU - Kozono, Hideo

AU - Shimizu, Senjo

PY - 2018/1/1

Y1 - 2018/1/1

N2 - We show existence theorem of global mild solutions with small initial data and external forces in the time-weighted Besov space which is an invariant space under the change of scaling. The result on local existence of solutions for large data is also discussed. Our method is based on the Lp-Lq estimate of the Stokes equations in Besov spaces. Since we construct the global solution by means of the implicit function theorem, as a byproduct, its stability with respect to the given data is necessarily obtained.

AB - We show existence theorem of global mild solutions with small initial data and external forces in the time-weighted Besov space which is an invariant space under the change of scaling. The result on local existence of solutions for large data is also discussed. Our method is based on the Lp-Lq estimate of the Stokes equations in Besov spaces. Since we construct the global solution by means of the implicit function theorem, as a byproduct, its stability with respect to the given data is necessarily obtained.

KW - 35Q30

KW - 76D03

KW - 76D05

KW - Global well-posedness

KW - Navier-Stokes equations

KW - Singular data

KW - Time-weighted Besov spaces

UR - http://www.scopus.com/inward/record.url?scp=85044759824&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85044759824&partnerID=8YFLogxK

U2 - 10.1002/mana.201700078

DO - 10.1002/mana.201700078

M3 - Article

AN - SCOPUS:85044759824

JO - Mathematische Nachrichten

JF - Mathematische Nachrichten

SN - 0025-584X

ER -