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...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.展开更多
基金Natural Science Foundation of Jiangsu Province for grant No.BK20180414National Natural Science Foundation of China for grant No.11801268Simons Foundation for grant No.710364.Xinghong Pan is supported by Natural Science Foundation of Jiangsu Province(No.BK20180414),Double Innovation Scheme of Jiangsu Province and National Natural Science Foundation of China(No.11801268).
文摘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.
