Global attractors of the delay 2D Navier-Stokes equations on unbounded Channel-like domains
Keywords:
Navier-Stokes equations, global attractors, uniform tail-ends estimatesAbstract
This paper studies the global attractors of 2D Navier-Stokes equations with delay defined in unbounded Channel-like domains. We establish the uniform tail-ends estimates of the solutions by establishing all the solutions are uniformly small for overcome the non-compactness of the solutions.
References
Wang B, Uniform tail-ends estimates of the Navier-Stokes equations on unbounded channel-like domains, Proceedings of the American Mathematical Society, 151(2023), no. 11, pp. 4841-4853, DOI org/10.1090/proc/16539. DOI: https://doi.org/10.1090/proc/16539
Caraballo T, Kukaszewioz G, Real J, Pullback attractors for non-autonomous 2D-Navier-Stokes equations in some un-bounded domains, Comptes Rendus Mathematique, 342(2006), no. 4, pp. 263-268. DOI 10.1016/j.crma.2005.12.015. DOI: https://doi.org/10.1016/j.crma.2005.12.015
Temam R, Navier-Stokes Equations: Theory and Numerical Analysis, North-Holland Publishing Co. Amsterdam-New York-Oxford, 1977.
Rosa R, The global attractor for the 2D Navier-Stokes flow on some unbounded domains, Nonlinear Anal. 32(1998), no. 1, pp. 71-85, DOI 10.1016/S0362-546X(97)00453-7. DOI: https://doi.org/10.1016/S0362-546X(97)00453-7
Ball, John, Global attractors for damped semilinear wave equations, Discrete and Continuous Dynamical Systems, 2003, DOI 10.3934/DCDS.2004.10.31. DOI: https://doi.org/10.3934/dcds.2004.10.31
Zdzisaw Brzeniak, Li Y, Asymptotic compactness and absorbing sets for 2D stochastic Navier-Stokes equations on some unbounded domains, Transactions of the American Mathematical Society, 385(2006), no. 12, pp. 5587-5629, DOI 10.2307/20161558. DOI: https://doi.org/10.1090/S0002-9947-06-03923-7
Lukaszewicz G, Sadowski W, Uniform attractor for 2D magneto-micropolar fluid flow in some unbounded domains, Zeitschrift f ¨ur angewandte Mathematik und Physik ZAMP, 55(2004), no. 2, pp. 247-257, DOI 10.1007/s00033-003-1127-7. DOI: https://doi.org/10.1007/s00033-003-1127-7
Moise I, Rosa R, Wang X, Attractors for noncompact nonautonomous systems via energy equations, Discrete Contin. Dyn Syst. 10(2004), no. 2, pp. 247-257, DOI 10.3934/dcds.2004.10.473. DOI: https://doi.org/10.3934/dcds.2004.10.473
Pedro Mar´ın-Rubio, Jos ´e Real, Attractors for 2D-Navier-Stokes equations with delays on some unbounded domains, Nonlinear Analysis. 67(2007), no. 10, pp. 2784-2799, DOI 10.1016/j.na.2006.09.035. DOI: https://doi.org/10.1016/j.na.2006.09.035
Wang B, Periodic random attractors for stochastic Navier-Stokes equations on unbounded domains, Electronic Journal of Differential Equations, 2012(2012), no. 59, DOI 10.1016/j.jmaa.2011.11.022.
Wang B, Attractors for reaction-diffusion equations in unbounded domains, Physica D Nonlinear Phenomena, 128(1999), no. 1, pp. 41-52, DOI 10.1016/S0167-2789(98)00304-2. DOI: https://doi.org/10.1016/S0167-2789(98)00304-2
Bates P W, Lu K, Wang B, Random attractors for stochastic reaction-diffusion equations on unbounded domains, Journal of Differential Equations, 246(2009), no. 2, pp. 845-869, DOI 10.1016/j.jde.2008.05.017. DOI: https://doi.org/10.1016/j.jde.2008.05.017
Wang X, Lu K, Wang B, Wong-Zakai approximations and attractors for stochastic reaction-diffusion equations on unbounded domains, Journal of Differential Equations, 2017:S0022039617304850, DOI 10.1016/j.jde.2017.09.006. DOI: https://doi.org/10.1016/j.jde.2017.09.006
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Copyright (c) 2024 Zhang Zhang, Xiaobin Yao (Corresponding Author)
This work is licensed under a Creative Commons Attribution 4.0 International License.
Accepted 2024 Mar 15
Published 2024 Mar 23