Previous |  Up |  Next

Article

Title: Global attractors for a tropical climate model (English)
Author: Han, Pigong
Author: Lei, Keke
Author: Liu, Chenggang
Author: Wang, Xuewen
Language: English
Journal: Applications of Mathematics
ISSN: 0862-7940 (print)
ISSN: 1572-9109 (online)
Volume: 68
Issue: 3
Year: 2023
Pages: 329-356
Summary lang: English
.
Category: math
.
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. (English)
Keyword: tropical climate model
Keyword: global attractor
Keyword: Hausdorff dimension
Keyword: fractal \hbox {dimension}
MSC: 35B40
MSC: 35Q35
MSC: 76D07
idZBL: Zbl 07729500
idMR: MR4586125
DOI: 10.21136/AM.2022.0230-21
.
Date available: 2023-05-04T17:38:23Z
Last updated: 2023-09-13
Stable URL: http://hdl.handle.net/10338.dmlcz/151657
.
Reference: [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. Zbl 0541.35038, MR 0710119, 10.1070/RM1983v038n04ABEH004209
Reference: [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. Zbl 1076.35089, MR 2153432, 10.1017/S0308210500003966
Reference: [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. Zbl 1062.35058, MR 2110209, 10.1016/j.jde.2004.09.011
Reference: [4] Brandolese, L.: Space-time decay of Navier-Stokes flows invariant under rotations.Math. Ann. 329 (2004), 685-706. Zbl 1080.35062, MR 2076682, 10.1007/s00208-004-0533-2
Reference: [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. Zbl 1085.37054, MR 2196010, 10.1016/j.crma.2005.12.015
Reference: [6] Chepyzhov, V. V., Vishik, M. I.: Attractors for Equations of Mathematical Physics.Colloquium Publications. American Mathematical Society 49. AMS, Providence (2002). Zbl 0986.35001, MR 1868930, 10.1090/coll/049
Reference: [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. Zbl 1406.35270, MR 3932724, 10.3934/dcdsb.2018102
Reference: [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. Zbl 1473.35438, MR 4281486, 10.1088/1361-6544/ac0d44
Reference: [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. Zbl 1415.86028, MR 3927105, 10.1007/s00332-018-9495-5
Reference: [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. Zbl 1160.86303, MR 2119930, 10.4310/CMS.2004.v2.n4.a3
Reference: [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). Zbl 1245.35002, MR 2808162, 10.1007/978-0-387-09620-9
Reference: [12] Ghidaglia, J. M., Temam, R.: Attractors for damped nonlinear hyperbolic equations.J. Math. Pures Appl., IX. Sér. 66 (1987), 273-319. Zbl 0572.35071, MR 0913856
Reference: [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. Zbl 1283.35009, MR 2573118, 10.1063/1.3227652
Reference: [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. Zbl 0982.35083, MR 1838503, 10.1017/S0308210500001013
Reference: [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. Zbl 1293.35245, MR 3198765, 10.1002/mma.2880
Reference: [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. Zbl 0327.35064, MR 0328378
Reference: [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. Zbl 1083.35094, MR 2153139, 10.3934/dcds.2005.13.701
Reference: [18] Schonbek, M. E.: $L^2$ decay for weak solutions of the Navier-Stokes equations.Arch. Ration. Mech. Anal. 88 (1985), 209-222. Zbl 0602.76031, MR 0775190, 10.1007/BF00752111
Reference: [19] Sermange, M., Temam, R.: Some mathematical questions related to the MHD equations.Commun. Pure Appl. Math. 36 (1983), 635-664. Zbl 0524.76099, MR 0716200, 10.1002/cpa.3160360506
Reference: [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. Zbl 1353.35097, MR 3554729, 10.1016/j.jmaa.2016.08.053
.

Fulltext not available (moving wall 24 months)

Partner of
EuDML logo