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Stabilization of 3D Navier–Stokes–Voigt equations

  • Cung The Anh EMAIL logo and Nguyen Viet Tuan

Abstract

We consider 3D Navier–Stokes–Voigt equations in smooth bounded domains with homogeneous Dirichlet boundary conditions. First, we study the existence and exponential stability of strong stationary solutions to the problem. Then we show that any unstable steady state can be exponentially stabilized by using either an internal feedback control with a support large enough or a multiplicative Itô noise of sufficient intensity.

MSC 2010: 35Q35; 35B40; 60H15

Award Identifier / Grant number: 101.02-2015.10

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

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Received: 2016-10-28
Revised: 2017-05-02
Accepted: 2017-08-13
Published Online: 2018-12-05
Published in Print: 2020-12-01

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