Time-periodic flow of a viscous liquid past a body

Giovanni P. Galdi, Mads Kyed

Research output: Chapter in Book/Report/Conference proceedingChapter

6 Citations (Scopus)


We investigate the existence, uniqueness and regularity of time-periodic solutions to the Navier-Stokes equations governing the flow of a viscous liquid past a three-dimensional body moving with a time-periodic translational velocity. The net motion of the body over a full time-period is assumed to be non-zero. In this case, the appropriate linearization is the time-periodic Oseen system in a three-dimensional exterior domain. A priori Lq estimates are established for this linearization. Based on these “maximal regularity” estimates, the existence and uniqueness of smooth solutions to the fully nonlinear Navier-Stokes problem is obtained by the contraction mapping principle.

Original languageEnglish
Title of host publicationPartial Differential Equations in Fluid Mechanics
PublisherCambridge University Press
Number of pages30
ISBN (Electronic)9781108610575
ISBN (Print)9781108460965
Publication statusPublished - 2019 Jan 1
Externally publishedYes


  • A priori estimates
  • Exterior domain
  • Navier-Stokes
  • Time-periodic Oseen system
  • Viscous liquid past a body

ASJC Scopus subject areas

  • Mathematics(all)


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