A Review of Results on Axially Symmetric Navier-Stokes Equations, with Addendum by X. Pan and Q. Zhang
Year: 2022
Author: Qi Zhang, Xinghong Pan
Analysis in Theory and Applications, Vol. 38 (2022), Iss. 3 : pp. 243–296
Abstract
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.
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/ata.OA-2020-0050
Analysis in Theory and Applications, Vol. 38 (2022), Iss. 3 : pp. 243–296
Published online: 2022-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 54
Keywords: Regularity Liouville theorem ancient solutions D-solutions axially symmetric Navier-Stokes equations.