On the asymptotic structure of steady Stokes and Navier-Stokes flows around a rotating two-dimensional body

Toshiaki Hishida, Mads Kyed

Research output: Contribution to journalArticlepeer-review

Abstract

We establish pointwise decay estimates for the velocity field of a steady two-dimensional Stokes flow around a rotating body via a new approach rather than analysis adopted in the previous literature [18], [20]. The novelty is to analyze the singular behavior of the constants in these estimates with respect to the angular velocity of the body, where such singularity is reasonable on account of the Stokes paradox. We then employ the estimates to identify the asymptotic structure at infinity of a steady scale-critical Navier-Stokes flow, being assumed to be small, around a rotating body. It is proved that the leading term is given by a self-similar Navier-Stokes flow which exhibits a circular profile x⊥/|x|2 and whose coefficient is the torque acting on the body.

35Q30, 76D05, 76D07, 35B40, 35C20

Original languageEnglish
JournalUnknown Journal
Publication statusPublished - 2018 Sep 10
Externally publishedYes

Keywords

  • Asymptotic expansion
  • Navier-Stokes
  • Rotating body
  • Stokes

ASJC Scopus subject areas

  • General

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