Time-periodic flow of a viscous liquid past a body

Giovanni P. Galdi, Mads Kyed

Research output: Chapter in Book/Report/Conference proceedingChapter

4 Citations (Scopus)

Abstract

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
Pages20-49
Number of pages30
ISBN (Electronic)9781108610575
ISBN (Print)9781108460965
DOIs
Publication statusPublished - 2019 Jan 1

Keywords

  • 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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