TY - JOUR

T1 - On the asymptotic structure of steady Stokes and Navier-Stokes flows around a rotating two-dimensional body

AU - Hishida, Toshiaki

AU - Kyed, Mads

N1 - Publisher Copyright:
Copyright © 2018, The Authors. All rights reserved.
Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.

PY - 2018/9/10

Y1 - 2018/9/10

N2 - 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

AB - 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

KW - Asymptotic expansion

KW - Navier-Stokes

KW - Rotating body

KW - Stokes

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M3 - Article

AN - SCOPUS:85092874457

JO - Nuclear Physics A

JF - Nuclear Physics A

SN - 0375-9474

ER -