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Abstract
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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. 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 since they cannot hold in the
absence of rotation. We then employ the estimates to identify the asymptotic
structure at infinity of a steady scale-critical Navier–Stokes flow, 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
and
whose coefficient is the torque acting on the body.
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Keywords
Navier–Stokes, Stokes, rotating body, asymptotic expansion
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Mathematical Subject Classification 2010
Primary: 35B40, 35C20, 35Q30, 76D05, 76D07
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Milestones
Received: 10 September 2018
Revised: 24 November 2020
Accepted: 6 September 2021
Published: 13 December 2021
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