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.

Author Details

Qi Zhang

Xinghong Pan