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Acta Mathematica Vietnamica

, Volume 42, Issue 2, pp 357–367 | Cite as

On the Stationary Solutions to 2D g-Navier-Stokes Equations

  • Dao Trong QuyetEmail author
  • Nguyen Viet Tuan
Article

Abstract

We consider g-Navier-Stokes equations in a two-dimensional smooth bounded domain Ω. First, we study the existence and exponential stability of a stationary solution under some certain conditions. Second, we prove that any unstable steady state can be stabilized by proportional controller with support in an open subset \(\omega \subset {\Omega }\) such that Ω∖ω is sufficiently “small.”

Keywords

g-Navier-Stokes equations Stationary solutions Stabilizable Feedback controller 

Mathematics Subject Classification (2010)

35B35 35Q35 35D35 

Notes

Acknowledgments

This research is funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grant number 101.02-2015.10.

The authors would like to thank Cung The Anh for suggestions and stimulating discussions on the subject of the paper.

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Copyright information

© Institute of Mathematics, Vietnam Academy of Science and Technology (VAST) and Springer Science+Business Media Singapore 2016

Authors and Affiliations

  1. 1.Faculty of Information TechnologyLe Quy Don Technical UniversityHanoiVietnam
  2. 2.Department of MathematicsSao Do UniversityHai DuongVietnam

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