The time periodic problem of the Navier–Stokes equations in a bounded domain with moving boundary

Reinhard Farwig, Hideo Kozono, Kazuyuki Tsuda, David Wegmann

Research output: Contribution to journalArticlepeer-review

Abstract

The time periodic problem of the Navier–Stokes equations on a non-cylindrical space–time domain is studied. Motivated by a recent result by Saal (2006) on maximal regularity for this kind of system we construct time periodic solutions in Lq-spaces provided the bounded domain moves periodically with small amplitude and the given periodic external force is small. The proof is based on new decay estimates for the solution operator of parabolic evolution equations corresponding to the non-cylindrical space–time domain problem.

Original languageEnglish
Article number103339
JournalNonlinear Analysis: Real World Applications
Volume61
DOIs
Publication statusPublished - 2021 Oct

Keywords

  • Moving boundary
  • Navier–Stokes equations
  • Non-cylindrical space–time domain
  • Time periodic problem
  • Uniform H-calculus

ASJC Scopus subject areas

  • Analysis
  • Engineering(all)
  • Economics, Econometrics and Finance(all)
  • Computational Mathematics
  • Applied Mathematics

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