A Review of Results on Axially Symmetric Navier-Stokes Equations, with Addendum by X. Pan and Q. Zhang (Analysis in Theory and Applications, 2022)
In this paper, we give a brief survey of recent results on axially symmetricNavier-Stokes equations (ASNS) in the following categories: regularity criterion, Liouville property for ancient solutions, decay and vanishing of stationary solutions. Somediscussions also touch on the full 3 dimensional equations. Two results, closing of thescaling gap for ASNS and vanishing of homogeneous D solutions in 3 dimensionalslabs will be described in more detail.In the addendum, two new results in the 3rd category will also be presented, whichare generalizations of recently published results by the author and coauthors.
Keywords: Regularity; Liouville theorem; ancient solutions; D-solutions; axially symmetric Navier-Stokes equations.