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axisymmetric solutions

Proceedings of the Royal Society of Edinburgh Section A: Mathematics (1)

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1 results

Axisymmetric flows in the exterior of a cylinder
Part of
- Partial differential equations
- Parabolic equations and systems
K. Abe, G. Seregin
Journal:

Proceedings of the Royal Society of Edinburgh. Section A: Mathematics / Volume 150 / Issue 4 / August 2020

Published online by Cambridge University Press:

01 February 2019, pp. 1671-1698

Print publication:

August 2020
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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 $ru^{\theta }_{0}\in L^{\infty }(\Pi )$.