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We study the stabilization of 2D $g$-Navier-Stokes equations in bounded domains with no-slip boundary conditions. First, we stabilize an unstable stationary solution by using finite-dimensional feedback controls, where the designed feedback control scheme is based on the finite number of determining parameters such as determining Fourier modes or volume elements. Second, we stabilize the long-time behavior of solutions to 2D $g$-Navier-Stokes equations under action of fast oscillating-in-time external forces by showing that in this case there exists a unique time-periodic solution and every solution tends to this periodic solution as time goes to infinity.
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참고문헌 (22)
참고문헌 신청
Cung The Anh / 2012 / Long-time behavior for 2D non-autonomous g-Navier–Stokes equations / Annales Polonici Mathematici 103(3):277~302
Cung The Anh / 2013 / Existence and finite time approximation of strong solutions to 2D g-Navier–Stokes equations / Acta Mathematica Vietnamica 38(3):413~428
Cung The Anh / 2017 / Stabilizing the long-time behavior of the Navier–Stokes–Voigt equations by fast oscillating-in-time forces / Bulletin of the Polish Academy of Sciences Mathematics 65(2):177~185
Abderrahim Azouani / 2014 / Feedback control of nonlinear dissipative systems by nite determining parameters|a reaction-diusion paradigm / Evolution Equations & Control Theory 3(4):579~594
Abderrahim Azouani / 2014 / Continuous Data Assimilation Using General Interpolant Observables / Journal of Nonlinear Science 24(2):277~304
Cung The Anh / 2013 / Existence and finite time approximation of strong solutions to 2D g-Navier–Stokes equations / Acta Mathematica Vietnamica 38(3):413~428
Cung The Anh / 2017 / Stabilizing the long-time behavior of the Navier–Stokes–Voigt equations by fast oscillating-in-time forces / Bulletin of the Polish Academy of Sciences Mathematics 65(2):177~185
Abderrahim Azouani / 2014 / Feedback control of nonlinear dissipative systems by nite determining parameters|a reaction-diusion paradigm / Evolution Equations & Control Theory 3(4):579~594
Abderrahim Azouani / 2014 / Continuous Data Assimilation Using General Interpolant Observables / Journal of Nonlinear Science 24(2):277~304
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