Asymptotic structure of a leray solution to the navier-stokes flow around a rotating body

Reinhard Farwig, Giovanni P. Galdi, Mads Kyed

Research output: Contribution to journalArticle

19 Citations (Scopus)

Abstract

Consider a body, B, rotating with constant angular velocity ω and fully submerged in a Navier-Stokes liquid that fills the whole space exterior to B. We analyze the flow of the liquid that is steady with respect to a frame attached to B. Our main theorem shows that the velocity field u of any weak solution (u p) in the sense of Leray has an asymptotic expansion with a suitable Landau solution as leading term and a remainder decaying pointwise like 1/ (x(1+αas (x(→∞for any α.∈(0,1), provided the magnitude of ω is below a positive constant depending on α.We also furnish analogous expansions for ▶u and for the corresponding pressure field p. These results improve and clarify a recent result of R. Farwig and T. Hishida.

Original languageEnglish
Pages (from-to)367-382
Number of pages16
JournalPacific Journal of Mathematics
Volume253
Issue number2
DOIs
Publication statusPublished - 2011
Externally publishedYes

Keywords

  • Asymptotic behavior of solutions
  • Navier-Stokes equations
  • Rotating frame

ASJC Scopus subject areas

  • Mathematics(all)

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