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

Matthias Georg Hieber, Thieu Huy Nguyen, Anton Seyfert

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 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 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.

Original languageEnglish
Title of host publicationMathematics for Nonlinear Phenomena—Analysis and Computation - In Honor of Yoshikazu Giga’s 60th Birthday
PublisherSpringer New York LLC
Pages51-81
Number of pages31
Volume215
ISBN (Print)9783319667621
DOIs
Publication statusPublished - 2017 Jan 1
Externally publishedYes
EventInternational 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 162015 Aug 18

Other

OtherInternational Conference on Mathematics for Nonlinear Phenomena: Analysis and Computation in Honor of Professor Yoshikazu Giga on his 60th Birthday, MNP 2015
CountryJapan
CitySapporo
Period15/8/1615/8/18

Fingerprint

Almost Periodic Solution
Almost Periodic
Viscous Flow
Viscous Fluid
Incompressible Fluid
Fluid Flow
Line
Navier-Stokes Equations
Oseen Equations
Semilinear Evolution Equation
Mild Solution
Interpolation Method
Incompressible Flow
Smoothing
Rotating
Generalise

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

Hieber, M. G., Nguyen, T. H., & 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, 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.

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 proceedingConference 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
Hieber MG, Nguyen TH, Seyfert A. 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. 2017. p. 51-81 https://doi.org/10.1007/978-3-319-66764-5_4
Hieber, Matthias Georg ; Nguyen, Thieu Huy ; Seyfert, Anton. / On periodic and almost periodic solutions to incompressible viscous fluid flow problems on the whole line. Mathematics for Nonlinear Phenomena—Analysis and Computation - In Honor of Yoshikazu Giga’s 60th Birthday. Vol. 215 Springer New York LLC, 2017. pp. 51-81
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