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Acta Mathematica Vietnamica

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

icon-email Dao Trong Quyet , Nguyen Viet Tuan

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 ωΩ such that Ωω is sufficiently “small.”