Asymptotic behavior for delay 2D Navier-Stokes equations on unbounded Channel-like domains

Yang Bai; Xiaobin  Yao

doi:10.61383/ejam.20242378

Authors

Yang Bai School of Mathematics and Statistics, Qinghai Minzu University, Xining, Qinghai, 810007, P.R. China Corresponding Author https://orcid.org/0009-0008-4318-9049
Xiaobin Yao School of Mathematics and Statistics, Qinghai Minzu University, Xining, Qinghai, 810007, P.R. China https://orcid.org/0000-0002-6170-9203

DOI:

https://doi.org/10.61383/ejam.20242378

Keywords:

Navier-Stokes equations, global attractors, uniform tail-ends estimates

Abstract

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

[1] Wang B. Uniform tail-ends estimates of the Navier-Stokes equations on unbounded channel-like domains. Proceedings of the American Mathematical Society, 151(2003),no. 11, pp.4841-4853.DOI org/10.1090/proc/16539. DOI: https://doi.org/10.1090/proc/16539

[2] 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.

[3] TemamR,Author, Chorin A ,et al.Navier Stokes Equations: Theory and Numerical Analysis. Journal of Applied Mechanics, 456(1984),no. 2, pp. 65-77. DOI 10.1115/1.3424338. DOI: https://doi.org/10.1115/1.3424338

[4] Rosa R. The global attractor for the 2D Navier-Stokes flow on some unbounded domains. Nonlinear Analy sis,32(1998),n0. 1,pp.71-85, DOI 10.1016/S0362-546X(97)00453-7. DOI: https://doi.org/10.1016/S0362-546X(97)00453-7

[5] 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

[6] 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

[7] Caraballo T, Lukaszewicz G, Real J.Pullback attractors for non-autonomous 2D-Navier–Stokes equations in some unbounded 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

[8] LUkaszewicz G, Sadowski W. Uniform attractor for 2D magneto-micropolar fluid flow in some unbounded do mains.Zeitschrift f¨ ur angewandte Mathematik und Physik ZAMP, 55(2004),no.2,pp.247-257,DOI 10.1007/s00033003-1127-7. DOI: https://doi.org/10.1007/s00033-003-1127-7

[9] Moise I, Rosa R, Wang X. Attractors for noncompact non-autonomous systems via energy equations. Discrete Contin. DynSyst. 10(2004),no.2,pp.247-257,DOI 10.3934/dcds.2004.10.473. DOI: https://doi.org/10.3934/dcds.2004.10.473

[10] 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

[11] 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.

[12] Wang B. Attractors for reaction-diffusion equations in unbounded domains. Physica D Nonlinear Phenom ena,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

[13] 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

[14] 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