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Axisymmetric flows in the exterior of a cylinder

Part of: Partial differential equations Parabolic equations and systems

Published online by Cambridge University Press:  01 February 2019

K. Abe  and
G. Seregin
K. Abe
Affiliation:
Department of Mathematics, Graduate School of Science, Osaka City University, Sugimoto 3-3-138, Sumiyoshi-ku Osaka558-8585, Japan (kabe@sci.osaka-cu.ac.jp)
G. Seregin
Affiliation:
Mathematical Institute, Oxford University, Oxford, 24-29 St Giles', OX1 3LB, UK and Voronezh State University, Voronezh, Russia (seregin@maths.ox.ac.uk)
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Abstract

We study an initial-boundary value problem of the three-dimensional Navier-Stokes equations in the exterior of a cylinder $\Pi =\{x=(x_{h}, x_3)\ \vert \vert x_{h} \vert \gt 1\}$, subject to the slip boundary condition. We construct unique global solutions for axisymmetric initial data $u_0\in L^{3}\cap L^{2}(\Pi )$ satisfying the decay condition of the swirl component $ru^{\theta }_{0}\in L^{\infty }(\Pi )$.

Keywords

Navier-Stokes equationsaxisymmetric solutionsexterior of a cylinder

MSC classification

Primary: 35B07: Axially symmetric solutions
Secondary: 35K20: Initial-boundary value problems for second-order parabolic equations 35K90: Abstract parabolic equations
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 150 , Issue 4 , August 2020 , pp. 1671 - 1698
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Copyright
Copyright © Royal Society of Edinburgh 2019

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