Axisymmetric flows in the exterior of a cylinder

Ken Abe; Gregory Seregin

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arXiv · 1708.00694

Axisymmetric flows in the exterior of a cylinder

Ken Abe·Gregory Seregin

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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 $\Pi=\{x=(x_{h}, x_3)\ |\ |x_{h} |>1\}$, 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 $ru^{\theta}_{0}\in L^{\infty}(\Pi)$.

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Ken Abe, Gregory Seregin. 2017-08-02. Axisymmetric flows in the exterior of a cylinder. https://arxiv.org/abs/1708.00694

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