Global strong solution of 3D tropical climate model with damping

Abstract

We establish the global well-posedness of a strong solution to the 3D tropical climate model with damping. We prove that there exists the global and unique solution for α, β, γ satisfying one of the following three conditions: (1) \alpha ,\beta \ge \mathrm{4}; (2) ; (3) .

Keywords

Tropical climate model (TCM) / damping / global regularity

References

[1] Cai X J, Jiu Q S. Weak and strong solutions for the incompressible Navier-Stokes equations with damping. J Math Anal Appl, 2008, 343(2): 799–809

[2] Dong B Q, Wang W J, Wu J H, Ye Z, Zhang H. Global regularity for a class of 2D generalized tropical climate models. J Differential Equations, 2019, 266(10): 6346–6382

[3] Dong B Q, Wang W J, Wu J H, Zhang H. Global regularity results for the climate model with fractional dissipation. Discrete Contin Dyn Syst Ser B, 2019, 24(1): 211–229

[4] Dong B Q, Wu J H, Ye Z. Global regularity for a 2D tropical climate model with fractional dissipation. J Nonlinear Sci, 2019, 29: 511-550

[5] Dong B Q, Wu J H, Ye Z. 2D tropical climate model with fractional dissipation and without thermal diffusion. Commun Math Sci, 2020, 18(1): 259–292

[6] Jiang Z H, Zhu M X. The large time behavior of solutions to 3D Navier-Stokes equations with nonlinear damping. Math Methods Appl Sci, 2012, 35(1): 97–102

[7] Li J K, Titi E S. Global well-posedness of strong solutions to a tropical climate model. Discrete Contin Dyn Syst, 2016, 36(8): 4495–4516

[8] Li J K, Yu Y H. Global regularity for a class of 3D tropical climate model without thermal diffusion. arXiv: 1905.04816[math.Ap]

[9] Liu H, Gao H J. Decay of solutions for the 3D Navier-Stokes equations with damping. Appl Math Lett, 2017, 68: 48–54

[10] Titi E S, Trabelsi S. Global well-posedness of a 3D MHD model in porous media. J Geom Mech, 2019, 11(4): 621–637

[11] Wan R H. Global small solutions to a tropical climate model without thermal diffusion. J Math Phys, 2016, 57(2): 1–13

[12] Wang W H, Zhou G P. Remarks on the regularity criterion of the Navier-Stokes equations with nonlinear damping. Math Probl Eng, 2015, 35: 1–5

[13] Wang Y N, Zhang S Y, Pan N N. Regularity and global existence on the 3D tropical climate model. Bull Malays Math Sci Soc, 2020, 43: 641–650

[14] Ye X, Zhu M X. Global strong solutions of the 2D tropical climate system with temperature-dependent viscosity. Z. Angew. Math. Phys, 2020, 71(3): 97–107

[15] Ye Z. Regularity and decay of 3D incompressible MHD equations with nonlinear damping terms. Colloq Math, 2015, 139(2): 185–203

[16] Ye Z. Global existence of strong solution to the 3D micropolar equations with a damping term. Appl Math Lett, 2018, 83: 188–193

[17] Zhang Z J, Wu C P, Yao Z A. Remarks on global regularity for the 3D MHD system with damping. Appl Math Comput, 2018, 333: 1–7

[18] Zhang Z J, Wu X L, Lu M. On the uniqueness of strong solution to the incompressible Navier-Stokes equations with damping. J Math Anal Appl, 2011, 377(1): 414–419

[19] Zhou Y. Regularity and uniqueness for the 3D imcompressible Navier-Stokes equations with damping. Appl Math Lett, 2012, 25(11): 1822–1825

[20] Zhu M X. Global regularity for the tropical climate model with fractional diffusion on barotropic model. Appl Math Lett, 2018, 81: 99–104

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Higher Education Press