### Abstract

Consider the equations of Navier–Stokes in ℝ^{3} in the rotational setting, i.e., with Coriolis force. It is shown that this set of equations admits a unique, global mild solution provided the initial data is small with respect to the norm of the Fourier–Besov space ḞB^{2−3/p} _{p,r} (ℝ^{3}), where p ∈ (1,∞] and r ∈ [1,∞]. In the two-dimensional setting, a unique, global mild solution to this set of equations exists for non-small initial data u_{0} ∈ L^{p} _{σ}(ℝ^{2}) for p ∈ [2,∞).

Original language | English |
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Title of host publication | Operator Theory: Advances and Applications |

Publisher | Springer International Publishing |

Pages | 199-211 |

Number of pages | 13 |

Volume | 250 |

Publication status | Published - 2015 |

Externally published | Yes |

### Publication series

Name | Operator Theory: Advances and Applications |
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Volume | 250 |

ISSN (Print) | 02550156 |

ISSN (Electronic) | 22964878 |

### Fingerprint

### Keywords

- Global existence
- Navier–Stokes
- Rotational framework

### ASJC Scopus subject areas

- Analysis

### Cite this

*Operator Theory: Advances and Applications*(Vol. 250, pp. 199-211). (Operator Theory: Advances and Applications; Vol. 250). Springer International Publishing.

**Global existence results for the Navier–Stokes equations in the rotational framework in Fourier–Besov spaces.** / Fang, Daoyuan; Han, Bin; Hieber, Matthias Georg.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

*Operator Theory: Advances and Applications.*vol. 250, Operator Theory: Advances and Applications, vol. 250, Springer International Publishing, pp. 199-211.

}

TY - CHAP

T1 - Global existence results for the Navier–Stokes equations in the rotational framework in Fourier–Besov spaces

AU - Fang, Daoyuan

AU - Han, Bin

AU - Hieber, Matthias Georg

PY - 2015

Y1 - 2015

N2 - Consider the equations of Navier–Stokes in ℝ3 in the rotational setting, i.e., with Coriolis force. It is shown that this set of equations admits a unique, global mild solution provided the initial data is small with respect to the norm of the Fourier–Besov space ḞB2−3/p p,r (ℝ3), where p ∈ (1,∞] and r ∈ [1,∞]. In the two-dimensional setting, a unique, global mild solution to this set of equations exists for non-small initial data u0 ∈ Lp σ(ℝ2) for p ∈ [2,∞).

AB - Consider the equations of Navier–Stokes in ℝ3 in the rotational setting, i.e., with Coriolis force. It is shown that this set of equations admits a unique, global mild solution provided the initial data is small with respect to the norm of the Fourier–Besov space ḞB2−3/p p,r (ℝ3), where p ∈ (1,∞] and r ∈ [1,∞]. In the two-dimensional setting, a unique, global mild solution to this set of equations exists for non-small initial data u0 ∈ Lp σ(ℝ2) for p ∈ [2,∞).

KW - Global existence

KW - Navier–Stokes

KW - Rotational framework

UR - http://www.scopus.com/inward/record.url?scp=84958980774&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84958980774&partnerID=8YFLogxK

M3 - Chapter

VL - 250

T3 - Operator Theory: Advances and Applications

SP - 199

EP - 211

BT - Operator Theory: Advances and Applications

PB - Springer International Publishing

ER -