The existence and regularity of time-periodic solutions to the three-dimensional Navier-Stokes equations in the whole space

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11 Citations (Scopus)

Abstract

The existence, uniqueness and regularity of time-periodic solutions to the Navier-Stokes equations in the three-dimensional whole space are investigated. We consider the Navier-Stokes equations with a non-zero drift term corresponding to the physical model of a fluid flow around a body that moves with a non-zero constant velocity. The existence of a strong time-periodic solution is shown for small time-periodic data. It is further shown that this solution is unique in a large class of weak solutions that can be considered physically reasonable. Finally, we establish regularity properties for any strong solution regardless of its size.

Original languageEnglish
Pages (from-to)2909-2935
Number of pages27
JournalNonlinearity
Volume27
Issue number12
DOIs
Publication statusPublished - 2014 Dec 1
Externally publishedYes

Keywords

  • Navier-Stokes
  • regularity
  • strong solutions
  • time-periodic
  • uniqueness

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Physics and Astronomy(all)
  • Applied Mathematics

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