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

Matthias Georg Hieber; Thieu Huy Nguyen; Anton Seyfert

doi:10.1007/978-3-319-66764-5_4

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

Matthias Georg Hieber^*, Thieu Huy Nguyen, Anton Seyfert

^*Corresponding author for this work

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

11 Citations (Scopus)

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
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	https://doi.org/10.1007/978-3-319-66764-5_4
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
Country/Territory	Japan
City	Sapporo
Period	15/8/16 → 15/8/18

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)

Access to Document

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

Cite this

On periodic and almost periodic solutions to incompressible viscous fluid flow problems on the whole line. / Hieber, Matthias Georg; Nguyen, Thieu Huy; Seyfert, Anton.
Mathematics for Nonlinear Phenomena—Analysis and Computation - In Honor of Yoshikazu Giga’s 60th Birthday. Vol. 215 Springer New York LLC, 2017. p. 51-81.

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

Hieber, MG, Nguyen, TH & Seyfert, A 2017, On periodic and almost periodic solutions to incompressible viscous fluid flow problems on the whole line. in 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

@inproceedings{6bdb3387f399429d8a25fbb389ea1991,

title = "On periodic and almost periodic solutions to incompressible viscous fluid flow problems on the whole line",

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 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.",

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

author = "Hieber, {Matthias Georg} and Nguyen, {Thieu Huy} and Anton Seyfert",

year = "2017",

month = jan,

day = "1",

doi = "10.1007/978-3-319-66764-5_4",

language = "English",

isbn = "9783319667621",

volume = "215",

pages = "51--81",

booktitle = "Mathematics for Nonlinear Phenomena—Analysis and Computation - In Honor of Yoshikazu Giga{\textquoteright}s 60th Birthday",

publisher = "Springer New York LLC",

note = "International Conference on Mathematics for Nonlinear Phenomena: Analysis and Computation in Honor of Professor Yoshikazu Giga on his 60th Birthday, MNP 2015 ; Conference date: 16-08-2015 Through 18-08-2015",

}

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

T2 - International Conference on Mathematics for Nonlinear Phenomena: Analysis and Computation in Honor of Professor Yoshikazu Giga on his 60th Birthday, MNP 2015

Y2 - 16 August 2015 through 18 August 2015

ER -

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

Abstract

Other

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this