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Keywords:
tropical climate model; global attractor; Hausdorff dimension; fractal \hbox {dimension}
Summary:
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.
References:
[1] Babin, A. V., Vishik, M. I.: 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. DOI 10.1070/RM1983v038n04ABEH004209 | MR 0710119 | Zbl 0541.35038
[2] Bae, H.-O., Jin, B. J.: Temporal and spatial decays for the Navier-Stokes equations. Proc. R. Soc. Edinb., Sect. A, Math. 135 (2005), 461-477. DOI 10.1017/S0308210500003966 | MR 2153432 | Zbl 1076.35089
[3] Bae, H.-O., Jin, B. J.: Upper and lower bounds of temporal and spatial decays for the Navier-Stokes equations. J. Differ. Equations 209 (2005), 365-391. DOI 10.1016/j.jde.2004.09.011 | MR 2110209 | Zbl 1062.35058
[4] Brandolese, L.: Space-time decay of Navier-Stokes flows invariant under rotations. Math. Ann. 329 (2004), 685-706. DOI 10.1007/s00208-004-0533-2 | MR 2076682 | Zbl 1080.35062
[5] Caraballo, T., Łukaszewicz, G., Real, J.: Pullback attractors for non-autonomous 2D-Navier-Stokes equations in some unbounded domains. C. R., Math., Acad. Sci. Paris 342 (2006), 263-268. DOI 10.1016/j.crma.2005.12.015 | MR 2196010 | Zbl 1085.37054
[6] Chepyzhov, V. V., Vishik, M. I.: Attractors for Equations of Mathematical Physics. Colloquium Publications. American Mathematical Society 49. AMS, Providence (2002). DOI 10.1090/coll/049 | MR 1868930 | Zbl 0986.35001
[7] Dong, B., Wang, W., Wu, J., Zhang, H.: Global regularity results for the climate model with fractional dissipation. Discrete Contin. Dyn. Syst., Ser. B 24 (2019), 211-229. DOI 10.3934/dcdsb.2018102 | MR 3932724 | Zbl 1406.35270
[8] Dong, B.-Q., Li, C., Xu, X., Ye, Z.: Global smooth solution of 2D temperature-dependent tropical climate model. Nonlinearity 34 (2021), 5662-5686. DOI 10.1088/1361-6544/ac0d44 | MR 4281486 | Zbl 1473.35438
[9] Dong, B.-Q., Wu, J., Ye, Z.: Global regularity for a 2D tropical climate model with fractional dissipation. J. Nonlinear Sci. 29 (2019), 511-550. DOI 10.1007/s00332-018-9495-5 | MR 3927105 | Zbl 1415.86028
[10] Frierson, D. M. W., Majda, A. J., Pauluis, O. M.: Large scale dynamics of precipitation fronts in the tropical atmosphere: A novel relaxation limit. Commun. Math. Sci. 2 (2004), 591-626. DOI 10.4310/CMS.2004.v2.n4.a3 | MR 2119930 | Zbl 1160.86303
[11] Galdi, G. P.: An Introduction to the Mathematical Theory of the Navier-Stokes Equations: Steady-State Problems. Springer Monographs in Mathematics. Springer, New York (2011). DOI 10.1007/978-0-387-09620-9 | MR 2808162 | Zbl 1245.35002
[12] Ghidaglia, J. M., Temam, R.: Attractors for damped nonlinear hyperbolic equations. J. Math. Pures Appl., IX. Sér. 66 (1987), 273-319. MR 0913856 | Zbl 0572.35071
[13] Gong, D., Song, H., Zhong, C.: Attractors for nonautonomous two-dimensional space periodic Navier-Stokes equations. J. Math. Phys. 50 (2009), Article ID 102706, 10 pages. DOI 10.1063/1.3227652 | MR 2573118 | Zbl 1283.35009
[14] He, C., Xin, Z.: On the decay properties of solutions to the non-stationary Navier-Stokes equations in $\mathbb R^3$. Proc. R. Soc. Edinb., Sect. A, Math. 131 (2001), 597-619. DOI 10.1017/S0308210500001013 | MR 1838503 | Zbl 0982.35083
[15] He, C., Zhou, D.: Existence and asymptotic behavior for an incompressible Newtonian flow with intrinsic degree of freedom. Math. Methods Appl. Sci. 37 (2014), 1191-1205. DOI 10.1002/mma.2880 | MR 3198765 | Zbl 1293.35245
[16] Ladyzhenskaya, O. A.: The dynamical system that is generated by the Navier-Stokes equations. Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Steklova 27 (1972), 91-115 Russian. MR 0328378 | Zbl 0327.35064
[17] Lu, S., Wu, H., Zhong, C.: Attractors for nonautonomous 2D Navier-Stokes equations with normal external forces. Discrete Contin. Dyn. Syst. 13 (2005), 701-719. DOI 10.3934/dcds.2005.13.701 | MR 2153139 | Zbl 1083.35094
[18] Schonbek, M. E.: $L^2$ decay for weak solutions of the Navier-Stokes equations. Arch. Ration. Mech. Anal. 88 (1985), 209-222. DOI 10.1007/BF00752111 | MR 0775190 | Zbl 0602.76031
[19] Sermange, M., Temam, R.: Some mathematical questions related to the MHD equations. Commun. Pure Appl. Math. 36 (1983), 635-664. DOI 10.1002/cpa.3160360506 | MR 0716200 | Zbl 0524.76099
[20] Ye, Z.: Global regularity for a class of 2D tropical climate model. J. Math. Anal. Appl. 446 (2017), 307-321 \99999DOI99999 10.1016/j.jmaa.2016.08.053 \goodbreak. DOI 10.1016/j.jmaa.2016.08.053 | MR 3554729 | Zbl 1353.35097
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