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Asymptotic behavior of solutions to stochastic 3D globally modified Navier-Stokes equations with unbounded delays

Cung The Anh|Vu Manh Toi|Phan Thi Tuyet
대한수학회 (The Korean Mathematical Society)|2024.03|대한수학회지 (Journal of the KMS)|제61권 제2호|pp. 227-253|DOI 10.4134/JKMS.j220380

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키워드

stabilityunbounded delaysstationary solutionspolynomial stability
주제분류수학

초록

This paper studies the existence of weak solutions and the stability of stationary solutions to stochastic 3D globally modified Navier-Stokes equations with unbounded delays in the phase space $BCL_{-\infty}(H)$. We first prove the existence and uniqueness of weak solutions by using the classical technique of Galerkin approximations. Then we study stability properties of stationary solutions by using several approach methods. In the case of proportional delays, some sufficient conditions ensuring the polynomial stability in both mean square and almost sure senses will be provided.

Abstract

This paper studies the existence of weak solutions and the stability of stationary solutions to stochastic 3D globally modified Navier-Stokes equations with unbounded delays in the phase space $BCL_{-\infty}(H)$. We first prove the existence and uniqueness of weak solutions by using the classical technique of Galerkin approximations. Then we study stability properties of stationary solutions by using several approach methods. In the case of proportional delays, some sufficient conditions ensuring the polynomial stability in both mean square and almost sure senses will be provided.

참고문헌 (25)

  1. C. T. Anh, "Asymptotic behaviour of solutions to stochastic three-dimensional globally modified Navier-Stokes equations", Stochastics, 95(6), pp.997~1021 (2023)[DOI]
  2. J. A. D. Appleby, "Sufficient conditions for polynomial asymptotic behaviour of the stochastic pantograph equation", Proceedings of the 10’th Colloquium on the Qualitative Theory of Differential Equations, 2, pp.32~ (2016)
  3. T. Caraballo, "Recent trends in dynamical systems", pp.473~492 (2013), Springer
  4. T. Caraballo, "Invariant measures and statistical solutions of the globally modified Navier-Stokes equations", Discrete Contin. Dyn. Syst. Ser. B, 10(4), pp.761~781 (2008)[DOI]
  5. T. Caraballo, "Unique strong solutions and V-attractors of a three dimensional system of globally modified Navier-Stokes equations", Adv. Nonlinear Stud, 6(3), pp.411~436 (2006)[DOI]
  6. G. Deugou´e, "On the time discretization for the globally modified three dimensional Navier-Stokes equations", J. Comput. Appl. Math, 235(8), pp.2015~2029 (2011)[DOI]
  7. G. Deugou´e, "The stochastic 3D globally modified Navier-Stokes equations: existence, uniqueness and asymptotic behavior", Commun. Pure Appl. Anal, 17(6), pp.2593~2621 (2018)[DOI]
  8. B. Q. Dong, "Global regularity and asymptotic behavior of modified Navier-Stokes equations with fractional dissipation", Discrete Contin. Dyn. Syst, 32(1), pp.57~79 (2012)[DOI]
  9. J. Duan, "Effective Dynamics of Stochastic Partial Differential Equations" (2014), Elsevier
  10. P. E. Kloeden, "Pullback V-attractors of the 3-dimensional globally modified Navier-Stokes equations", Commun. Pure Appl. Anal, 6(4), pp.937~955 (2007)[DOI]
  11. P. E. Kloeden, "Equivalence of invariant measures and stationary statistical solutions for the autonomous globally modified Navier-Stokes equations", Commun. Pure Appl. Anal, 8(3), pp.785~802 (2009)[DOI]
  12. L. F. Liu, "Analysis of a stochastic 2D-Navier-Stokes model with infinite delay", J. Dynam. Differential Equations, 31(4), pp.2249~2274 (2019)[DOI]
  13. L. F. Liu, "Stability results for 2D Navier-Stokes equations with unbounded delay", J. Differential Equations, 265(11), pp.5685~5708 (2018)[DOI]
  14. P. Mar´ın-Rubio, "Three dimensional system of globally modified Navier-Stokes equations with infinite delays", Discrete Contin. Dyn. Syst. Ser. B, 14(2), pp.655~673 (2010)[DOI]
  15. P. Mar´ın-Rubio, "Pullback attractors for globally modified Navier-Stokes equations with infinite delays", Discrete Contin. Dyn. Syst, 31(3), pp.779~796 (2011)[DOI]
  16. P. Mar´ın-Rubio, "Asymptotic behavior of solutions for a three dimensional system of globally modified Navier-Stokes equations with a locally Lipschitz delay term", Nonlinear Anal, 79, pp.68~79 (2013)[DOI]
  17. P. Mar´ın-Rubio, "On the convergence of solutions of globally modified Navier-Stokes equations with delays to solutions of Navier-Stokes equations with delays", Adv. Nonlinear Stud, 11(4), pp.917~927 (2011)[DOI]
  18. M. Romito, "The uniqueness of weak solutions of the globally modified Navier-Stokes equations", Adv. Nonlinear Stud, 9(2), pp.425~427 (2009)[DOI]
  19. L. T. Thuy, "Asymptotic behavior of solutions to 3D Kelvin-Voigt-Brinkman-Forchheimer equations with unbounded delays", Electron. J. Differential Equations, 2022(7), pp.18~ (2022)[DOI]
  20. V. M. Toi, "Stability and stabilization for the three-dimensional Navier-Stokes-Voigt equations with unbounded variable delay", Evol. Equ. Control Theory, 10(4), pp.1007~1023 (2021)[DOI]
  21. J. Wang, "Invariant measures for the 3D globally modified Navier-Stokes equations with unbounded variable delays", Commun. Nonlinear Sci. Numer. Simul, 91(105459), pp.14~ (2020)[DOI]
  22. F. Wei, "The existence and uniqueness of the solution for stochastic functional differential equations with infinite delay", J. Math. Anal. Appl, 331(1), pp.516~531 (2007)[DOI]
  23. F. Wu, "Stochastic functional differential equations with infinite delay: existence and uniqueness of solutions, solution maps, Markov properties, and ergodicity", J. Differential Equations, 262(3), pp.1226~1252 (2017)[DOI]
  24. C. Zhao, "Asymptotic regularity of trajectory attractor and trajectory statistical solution for the 3D globally modified Navier-Stokes equations", J. Differential Equations, 266(11), pp.7205~7229 (2019)[DOI]
  25. C. Zhao, "Pullback attractors and invariant measures for the nonautonomous globally modified Navier-Stokes equations", Commun. Math. Sci, 15(6), pp.1565~1580 (2017)[DOI]

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Dynamics of solutions for the three-dimensional stochastic globally modified Navier-Stokes equations on unbounded domainsBui Kim My, Ho Thi Hang, Pham Tri Nguyen대한수학회 · 대한수학회보2024 · 제61권 제5호Existence and long-time behavior of solutions to Navier-Stokes-Voigt equations with infinite delayCung The Anh, Dang Thi Phuong Thanh대한수학회 · 대한수학회보2018 · 제55권 제2호Pullback attractors for 2D $g$-Navier-Stokes equations with infinite delaysDao Trong Quyet대한수학회 · 대한수학회논문집2016 · 제31권 제3호Existence of random attractors for stochastic non-autonomous reaction-diffusion equation with multiplicative noise on $\mathbb{R}^{n}$Fadlallah Mustafa Mosa, Mohamed Y. A. Bakhet, Qiaozhen Ma강원경기수학회 · 한국수학논문집2018 · 제26권 제4호Asymptotic behavior of solutions to 3D convective Brinkman-Forchheimer equations with finite delaysLe Thi Thuy대한수학회 · 대한수학회논문집2021 · 제36권 제3호Random attractor for stochastic partial functional differential equations with infinite delayHonglian You, Rong Yuan대한수학회 · 대한수학회보2014 · 제51권 제5호

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