Asymptotic stability of homogeneous solutions of incompressible stationary Navier-Stokes equations
Asymptotic stability of homogeneous solutions of incompressible stationary Navier-Stokes equations
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DOI：
10.1016/j.jde.2021.06.033
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发表时间：
2019-11
期刊：
影响因子：
--
通讯作者：
Y. Li;Xukai Yan
中科院分区：
文献类型：
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作者：
Y. Li;Xukai Yan
Karch和Pilarczyk证明了朗道解在任何L2-扰动下都是渐近稳定的.在我们与L. Li，我们对三维不可压定常Navier-Stokes方程的所有（-1）-齐次轴对称无旋解进行了分类，这些解在单位球面上减去南北极是光滑的。本文研究了这些解中除朗道解以外的最小奇异解的渐近稳定性，证明了这类解在任何L 2-扰动下都是渐近稳定的。
It was proved by Karch and Pilarczyk that Landau solutions are asymptotically stable under any L 2-perturbation. In our earlier work with L. Li, we have classified all (− 1)-homogeneous axisymmetric no-swirl solutions of incompressible stationary Navier-Stokes equations in three dimension which are smooth on the unit sphere minus the south and north poles. In this paper, we study the asymptotic stability of the least singular solutions among these solutions other than Landau solutions, and prove that such solutions are asymptotically stable under any L 2-perturbation.