Global Strong Solutions to the Inhomogeneous Incompressible Navier-Stokes System in the Exterior of a Cylinder

Global Strong Solutions to the Inhomogeneous Incompressible Navier-Stokes System in the Exterior of a Cylinder
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DOI：
10.1137/20m1384439
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发表时间：
2020-04
期刊：
SIAM J. Math. Anal.
影响因子：
--
通讯作者：
Zhengguang Guo;Yun Wang;Chunjing Xie
Zhengguang Guo;Yun Wang;Chunjing Xie
中科院分区：
其他
文献类型：
--
作者：
Zhengguang Guo;Yun Wang;Chunjing Xie

文献摘要

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本文在Dirichlet边界条件下，建立了圆柱外非齐次不可压Navier-Stokes方程组的整体强轴对称解。此外，在这些溶液中允许真空。分析的关键要素之一是获得速度场的${L^{2}（s，T;L^{\infty}（\Omega））}$界，其中解的轴对称性起着重要作用。
In this paper, the global strong axisymmetric solutions for the inhomogeneous incompressible Navier-Stokes system are established in the exterior of a cylinder subject to the Dirichlet boundary conditions. Moreover, the vacuum is allowed in these solutions. One of the key ingredients of the analysis is to obtain the ${L^{2}(s,T;L^{\infty}(\Omega))}$ bound for the velocity field, where the axisymmetry of the solutions plays an important role.