Stability and stabilization for the three-dimensional Navier-Stokes-Voigt equations with unbounded variable delay

Vu Manh Toi

doi:10.3934/eect.2020099

Article Contents

2021, Volume 10, Issue 4: 1007-1023. Doi: 10.3934/eect.2020099

This issue Previous Article Well-posedness of linear first order port-Hamiltonian Systems on multidimensional spatial domains Next Article

Stability and stabilization for the three-dimensional Navier-Stokes-Voigt equations with unbounded variable delay

Vu Manh Toi

Faculty of Computer Science and Engineering, Thuyloi University, 175 Tay Son, Dong Da, Hanoi, Vietnam

Received: February 28, 2019

Revised: August 31, 2020

Early access: October 2020

Published: December 2021

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Abstract

We consider the 3D Navier-Stokes-Voigt equations in a bounded domain with unbounded variable delay. We study the stability of stationary solutions by the classical direct method, and by an appropriate Lyapunov functional. We also give a sufficient condition of parameters for the polynomial stability of the stationary solution in a special case of unbounded variable delay. Finally, when the condition for polynomial stability is not satisfied, we stabilize the stationary by using the finite Fourier modes and by internal feedback control with a support large enough.

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Mathematics Subject Classification: 35Q35, 35Q30, 35B35, 35B40, 35A01, 93D15.

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