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In this paper, we give a brief survey of recent results on axially symmetricNavier-Stokes equations (ASNS) in the following categories: regularitycriterion, Liouville property for ancient solutions, decay and vanishing ofstationary solutions. Some discussions also touch on the full 3 dimensionalequations. Two results, closing of the scaling gap for ASNS and vanishing ofhomogeneous D solutions in 3 dimensional slabs will be described in moredetail. In the addendum, two new results in the 3rd category will also bepresented, which are generalizations of recently published results by theauthor and coauthors.

A Review of results on axially symmetric Navier-Stokes equations, with addendum by X. Pan and Q. S. Zhang