Abstract
This paper is devoted to the global attractors of the tropical climate model. We first establish the global well-posedness of the system. Then by studying the existence of bounded absorbing sets, the global attractor is constructed. The estimates of the Hausdorff dimension and of the fractal dimension of the global attractor are obtained in the end.
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A. V. Babin, M. I. Vishik: Attractors of partial differential evolution equations and estimates of their dimension. Russ. Math. Surv. 38 (1983), 151–213; translation from Usp. Mat. Nauk 38 (1983), 133–187.
H.-O. Bae, B. J. Jin: Temporal and spatial decays for the Navier-Stokes equations. Proc. R. Soc. Edinb., Sect. A, Math. 135 (2005), 461–477.
H.-O. Bae, B. J. Jin: Upper and lower bounds of temporal and spatial decays for the Navier-Stokes equations. J. Differ. Equations 209 (2005), 365–391.
L. Brandolese: Space-time decay of Navier-Stokes flows invariant under rotations. Math. Ann. 329 (2004), 685–706.
T. Caraballo, G. Łukaszewicz, J. Real: Pullback attractors for non-autonomous 2D-Navier-Stokes equations in some unbounded domains. C. R., Math., Acad. Sci. Paris 342 (2006), 263–268.
V. V. Chepyzhov, M. I. Vishik: Attractors for Equations of Mathematical Physics. Colloquium Publications. American Mathematical Society 49. AMS, Providence, 2002.
B. Dong, W. Wang, J. Wu, H. Zhang: Global regularity results for the climate model with fractional dissipation. Discrete Contin. Dyn. Syst., Ser. B 24 (2019), 211–229.
B.-Q. Dong, C. Li, X. Xu, Z. Ye: Global smooth solution of 2D temperature-dependent tropical climate model. Nonlinearity 34 (2021), 5662–5686.
B.-Q. Dong, J. Wu, Z. Ye: Global regularity for a 2D tropical climate model with fractional dissipation. J. Nonlinear Sci. 29 (2019), 511–550.
D. M. W. Frierson, A. J. Majda, O. M. Pauluis: Large scale dynamics of precipitation fronts in the tropical atmosphere: A novel relaxation limit. Commun. Math. Sci. 2 (2004), 591–626.
G. P. Galdi: An Introduction to the Mathematical Theory of the Navier-Stokes Equations: Steady-State Problems. Springer Monographs in Mathematics. Springer, New York, 2011.
J. M. Ghidaglia, R. Temam: Attractors for damped nonlinear hyperbolic equations. J. Math. Pures Appl., IX. Sér. 66 (1987), 273–319.
D. Gong, H. Song, C. Zhong: Attractors for nonautonomous two-dimensional space periodic Navier-Stokes equations. J. Math. Phys. 50 (2009), Article ID 102706, 10 pages.
C. He, Z. Xin: On the decay properties of solutions to the non-stationary Navier-Stokes equations in ℝ3. Proc. R. Soc. Edinb., Sect. A, Math. 131 (2001), 597–619.
C. He, D. Zhou: Existence and asymptotic behavior for an incompressible Newtonian flow with intrinsic degree of freedom. Math. Methods Appl. Sci. 37 (2014), 1191–1205.
O. A. Ladyzhenskaya: The dynamical system that is generated by the Navier-Stokes equations. Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Steklova 27 (1972), 91–115. (In Russian.)
S. Lu, H. Wu, C. Zhong: Attractors for nonautonomous 2D Navier-Stokes equations with normal external forces. Discrete Contin. Dyn. Syst. 13 (2005), 701–719.
M. E. Schonbek: L2 decay for weak solutions of the Navier-Stokes equations. Arch. Ration. Mech. Anal. 88 (1985), 209–222.
M. Sermange, R. Temam: Some mathematical questions related to the MHD equations. Commun. Pure Appl. Math. 36 (1983), 635–664.
Z. Ye: Global regularity for a class of 2D tropical climate model. J. Math. Anal. Appl. 446 (2017), 307–321.
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This work is supported by the National Key R&D Program of China (2021YFA1000800), the National Natural Science Foundation of China under Grant No. 11871457, the K. C. Wong Education Foundation, Chinese Academy of Sciences.
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Han, P., Lei, K., Liu, C. et al. Global attractors for a tropical climate model. Appl Math 68, 329–356 (2023). https://doi.org/10.21136/AM.2022.0230-21
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DOI: https://doi.org/10.21136/AM.2022.0230-21