轴对称Navier-Stokes方程结果的评述,附潘X.和张强的补编

IF 0.4 Q4 MATHEMATICS Analysis in Theory and Applications Pub Date : 2021-01-13 DOI:10.4208/ata.oa-2020-0050
Qi S. Zhang
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引用次数: 1

摘要

本文简要综述了轴对称Navier-Stokes方程在正则性判据、古解的Liouville性质、平稳解的衰减和消失等方面的最新研究成果。一些讨论也涉及到完整的三维方程。两个结果,关闭尺度差距的ASNS和消失的均匀D溶液在三维板将更详细地描述。在增编中,还将介绍第三类的两个新结果,它们是作者及其合著者最近发表的结果的概括。
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A Review of Results on Axially Symmetric Navier-Stokes Equations, with Addendum by X. Pan and Q. Zhang
In this paper, we give a brief survey of recent results on axially symmetric Navier-Stokes equations (ASNS) in the following categories: regularity criterion, Liouville property for ancient solutions, decay and vanishing of stationary solutions. Some discussions also touch on the full 3 dimensional equations. Two results, closing of the scaling gap for ASNS and vanishing of homogeneous D solutions in 3 dimensional slabs will be described in more detail. In the addendum, two new results in the 3rd category will also be presented, which are generalizations of recently published results by the author and coauthors.
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