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Stabilization of 2D $g$-Navier-Stokes equations

Nguyen Viet Tuan
대한수학회 (The Korean Mathematical Society)|2019.07|대한수학회논문집 (Communications of the KMS)|제34권 제3호|pp. 819-839|DOI 10.4134/CKMS.c180265

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키워드

stabilizationstationary solution2D $g$-Navier-Stokes equationstime-periodic solutionfinite-dimensional feedback controlsoscillating-in-time forces
주제분류수학

초록

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.

Abstract

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.

참고문헌 (22)

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관련 논문AI추천

ASYMPTOTIC BEHAVIOR OF STRONG SOLUTIONS TO 2D g-NAVIER-STOKES EQUATIONSDao Trong Quyet대한수학회 · 대한수학회논문집2014 · 제29권 제4호On the finite-dimensional global attractor for the Navier-Stokes-$\alpha$-Boussinesq modelLe Thi Thuy, Tran Quang Thinh, Vu Manh Toi대한수학회 · 대한수학회보2025 · 제62권 제6호A boundary control problem for vorticity minimization in time-dependent 2D Navier-Stokes equations김홍철강원경기수학회 · 한국수학논문집2015 · 제23권 제2호Pullback attractors for 2D $g$-Navier-Stokes equations with infinite delaysDao Trong Quyet대한수학회 · 대한수학회논문집2016 · 제31권 제3호The Global Attractor of the 2D g-Navier-Stokes Equations on some unbounded domains권혁진, 노재옥대한수학회 · 대한수학회논문집2005 · 제20권 제4호Global existence for 3D Navier-Stokes equations in a long periodic domain곽민규, 김남권대한수학회 · 대한수학회지2012 · 제49권 제2호

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