### Abstract

It is shown that a large class of semilinear evolution equations on the whole line with periodic or almost periodic forces admit periodic or almost periodic mild solutions. The approach presented generalizes the method described in [28] to the case of the whole line and to forces which are almost periodic in the sense of H. Bohr. It relies on interpolation methods and on L^{p}- L^{q} -smoothing properties of the underlying linearized equation. Applied to incompressible fluid flow problems, the approach yields new results on (almost) periodic solutions to the Navier-Stokes-Oseen equations, to the flow past rotating obstacles, to the Navier-Stokes equations in the rotational setting as well as to Ornstein–Uhlenbeck type equations.

Original language | English |
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Title of host publication | Mathematics for Nonlinear Phenomena—Analysis and Computation - In Honor of Yoshikazu Giga’s 60th Birthday |

Publisher | Springer New York LLC |

Pages | 51-81 |

Number of pages | 31 |

Volume | 215 |

ISBN (Print) | 9783319667621 |

DOIs | |

Publication status | Published - 2017 Jan 1 |

Externally published | Yes |

Event | International Conference on Mathematics for Nonlinear Phenomena: Analysis and Computation in Honor of Professor Yoshikazu Giga on his 60th Birthday, MNP 2015 - Sapporo, Japan Duration: 2015 Aug 16 → 2015 Aug 18 |

### Other

Other | International Conference on Mathematics for Nonlinear Phenomena: Analysis and Computation in Honor of Professor Yoshikazu Giga on his 60th Birthday, MNP 2015 |
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Country | Japan |

City | Sapporo |

Period | 15/8/16 → 15/8/18 |

### Fingerprint

### Keywords

- Flow past rotating obstacles
- Incompressible fluid flow
- Navier-Stokes-Coriolis equations
- Navier-Stokes-Oseen equations
- Periodoc and almost periodic solutions
- Semilinear evolution equations

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Mathematics for Nonlinear Phenomena—Analysis and Computation - In Honor of Yoshikazu Giga’s 60th Birthday*(Vol. 215, pp. 51-81). Springer New York LLC. https://doi.org/10.1007/978-3-319-66764-5_4

**On periodic and almost periodic solutions to incompressible viscous fluid flow problems on the whole line.** / Hieber, Matthias Georg; Nguyen, Thieu Huy; Seyfert, Anton.

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

*Mathematics for Nonlinear Phenomena—Analysis and Computation - In Honor of Yoshikazu Giga’s 60th Birthday.*vol. 215, Springer New York LLC, pp. 51-81, International Conference on Mathematics for Nonlinear Phenomena: Analysis and Computation in Honor of Professor Yoshikazu Giga on his 60th Birthday, MNP 2015, Sapporo, Japan, 15/8/16. https://doi.org/10.1007/978-3-319-66764-5_4

}

TY - GEN

T1 - On periodic and almost periodic solutions to incompressible viscous fluid flow problems on the whole line

AU - Hieber, Matthias Georg

AU - Nguyen, Thieu Huy

AU - Seyfert, Anton

PY - 2017/1/1

Y1 - 2017/1/1

N2 - It is shown that a large class of semilinear evolution equations on the whole line with periodic or almost periodic forces admit periodic or almost periodic mild solutions. The approach presented generalizes the method described in [28] to the case of the whole line and to forces which are almost periodic in the sense of H. Bohr. It relies on interpolation methods and on Lp- Lq -smoothing properties of the underlying linearized equation. Applied to incompressible fluid flow problems, the approach yields new results on (almost) periodic solutions to the Navier-Stokes-Oseen equations, to the flow past rotating obstacles, to the Navier-Stokes equations in the rotational setting as well as to Ornstein–Uhlenbeck type equations.

AB - It is shown that a large class of semilinear evolution equations on the whole line with periodic or almost periodic forces admit periodic or almost periodic mild solutions. The approach presented generalizes the method described in [28] to the case of the whole line and to forces which are almost periodic in the sense of H. Bohr. It relies on interpolation methods and on Lp- Lq -smoothing properties of the underlying linearized equation. Applied to incompressible fluid flow problems, the approach yields new results on (almost) periodic solutions to the Navier-Stokes-Oseen equations, to the flow past rotating obstacles, to the Navier-Stokes equations in the rotational setting as well as to Ornstein–Uhlenbeck type equations.

KW - Flow past rotating obstacles

KW - Incompressible fluid flow

KW - Navier-Stokes-Coriolis equations

KW - Navier-Stokes-Oseen equations

KW - Periodoc and almost periodic solutions

KW - Semilinear evolution equations

UR - http://www.scopus.com/inward/record.url?scp=85034233018&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85034233018&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-66764-5_4

DO - 10.1007/978-3-319-66764-5_4

M3 - Conference contribution

AN - SCOPUS:85034233018

SN - 9783319667621

VL - 215

SP - 51

EP - 81

BT - Mathematics for Nonlinear Phenomena—Analysis and Computation - In Honor of Yoshikazu Giga’s 60th Birthday

PB - Springer New York LLC

ER -