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.”
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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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Quyet, D.T., Tuan, N.V. On the Stationary Solutions to 2D g-Navier-Stokes Equations. Acta Math Vietnam 42, 357–367 (2017). https://doi.org/10.1007/s40306-016-0180-1
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DOI: https://doi.org/10.1007/s40306-016-0180-1