Viscous Flow Around a Rigid Body Performing a Time-periodic Motion

Thomas Eiter*, Mads Kyed

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)


The equations governing the flow of a viscous incompressible fluid around a rigid body that performs a prescribed time-periodic motion with constant axes of translation and rotation are investigated. Under the assumption that the period and the angular velocity of the prescribed rigid-body motion are compatible, and that the mean translational velocity is non-zero, existence of a time-periodic solution is established. The proof is based on an appropriate linearization, which is examined within a setting of absolutely convergent Fourier series. Since the corresponding resolvent problem is ill-posed in classical Sobolev spaces, a linear theory is developed in a framework of homogeneous Sobolev spaces.

Original languageEnglish
Article number28
JournalJournal of Mathematical Fluid Mechanics
Issue number1
Publication statusPublished - 2021 Feb


  • Navier-Stokes
  • Oseen flow
  • Rotating obstacles
  • Time-periodic solutions

ASJC Scopus subject areas

  • Mathematical Physics
  • Condensed Matter Physics
  • Computational Mathematics
  • Applied Mathematics


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