# American Institute of Mathematical Sciences

October  2017, 37(10): 5065-5083. doi: 10.3934/dcds.2017219

## The global stability of 2-D viscous axisymmetric circulatory flows

 1 School of Mathematical Sciences, Nanjing Normal University, Nanjing 210023, China 2 Department of Mathematics and IMS, Nanjing University, Nanjing 210093, China

* Corresponding author: Lin Zhang

Received  February 2015 Revised  May 2017 Published  June 2017

Fund Project: The authors are supported by the NSFC (No. 11571177) and A Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions.

In this paper, we study the global existence and stability problem of a perturbed viscous circulatory flow around a disc. This flow is described by two-dimensional Navier-Stokes equations. By introducing some suitable weighted energy space and establishing a priori estimates, we show that the 2-D circulatory flow is globally stable in time when the corresponding initial-boundary values are perturbed sufficiently small.

Citation: Huicheng Yin, Lin Zhang. The global stability of 2-D viscous axisymmetric circulatory flows. Discrete & Continuous Dynamical Systems, 2017, 37 (10) : 5065-5083. doi: 10.3934/dcds.2017219
##### References:

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##### References:
Subsonic case of a viscous flow around a disc
Supersonic-sonic-subsonic case of a viscous flow around a disc
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