Vol. 315, No. 1, 2021

Download this article
Download this article For screen
For printing
Recent Issues
Vol. 320: 1
Vol. 319: 1  2
Vol. 318: 1  2
Vol. 317: 1  2
Vol. 316: 1  2
Vol. 315: 1  2
Vol. 314: 1  2
Vol. 313: 1  2
Online Archive
The Journal
Editorial Board
Submission Guidelines
Submission Form
Policies for Authors
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Special Issues
Author Index
To Appear
Other MSP Journals
This article is available for purchase or by subscription. See below.
On the asymptotic structure of steady Stokes and Navier–Stokes flows around a rotating two-dimensional body

Toshiaki Hishida and Mads Kyed

Vol. 315 (2021), No. 1, 89–109

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 x|x|2 and whose coefficient is the torque acting on the body.

PDF Access Denied

We have not been able to recognize your IP address as that of a subscriber to this journal.
Online access to the content of recent issues is by subscription, or purchase of single articles.

Please contact your institution's librarian suggesting a subscription, for example by using our journal-recom­mendation form. Or, visit our subscription page for instructions on purchasing a subscription.

You may also contact us at contact@msp.org
or by using our contact form.

Or, you may purchase this single article for USD 40.00:

Navier–Stokes, Stokes, rotating body, asymptotic expansion
Mathematical Subject Classification 2010
Primary: 35B40, 35C20, 35Q30, 76D05, 76D07
Received: 10 September 2018
Revised: 24 November 2020
Accepted: 6 September 2021
Published: 13 December 2021
Toshiaki Hishida
Graduate School of Mathematics
Nagoya University
Mads Kyed
Flensburg University of Applied Sciences
Faculty of Science and Engineering
Waseda University