Open AccessStability and stabilization for the three-dimensional Navier-Stokes-Voigt equations with unbounded variable delay
Author(s) -
Vu Manh Toi
Publication year - 2021
Publication title -
evolution equations and control theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.665
H-Index - 19
eISSN - 2163-2480
pISSN - 2163-2472
DOI - 10.3934/eect.2020099
Subject(s) - bounded function , mathematics , polynomial , stability (learning theory) , variable (mathematics) , domain (mathematical analysis) , mathematical analysis , computer science , machine learning
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.