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Global Well-Posedness of the Fractional tropical climate model

Journal of Applied Mathematics and Physics 2024年第3期12卷 805-818页

作者： Meiqi Hu College of Mathematicals Science Zhejiang Normal University Jinhua China College of Data Science Jiaxing University Jiaxing China

In this paper, we consider the Cauchy problem of 3-dimensional tropical climate model. This model reflects the interaction and coupling among the barotropic mode u, the first baroclinic mode v of the velocity and the temperature θ. The systems with fractional dissipation studied here may arise in the modeling of geophysical circumstances. Mathematically these systems allow simultaneous examination of a family of systems with various levels of regularization. The aim here is the global strong solution with the least dissipation. By energy estimate and delicate analysis, we prove the existence of global solution under three different cases: first, with the help of damping terms, the global strong solution of the system with Λ2au, Λ2βv and Λ2γ θ for;and second, the global strong solution of the system for with damping terms;finally, the global strong solution of the system for without any damping terms, which improve the known existence theory for this system.

关键词： tropical climate model Fractional Diffusion Global Existence

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Global Strong Solutions and Large-time Behavior of 2D tropical climate model

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应用数学学报:英文版 2023年第4期39卷 886-925页

作者： Dong-juan NIU Ying WANG School of Mathematical Sciences Capital Normal UniversityBeijing 100048China School of Physical Science and Technology Guangxi UniversityNanning 530004China

In this paper we mainly deal with the global well-posedness and large-time behavior of the 2D tropical climate model with small initial data. We first establish the global well-posedness of solution in the Besov space, then we obtain the optimal decay rates of solutions by virtue of the frequency decomposition method. Specifically, for the low frequency part, we use the Fourier splitting method of Schonbek and the spectrum analysis method, and for the high frequency part, we use the global energy estimate and the behavior of exponentially decay operator.

关键词： tropical climate model large-time behavior global well-posedness

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Global Well-Posedness for the 3D tropical climate model without Thermal Diffusion

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Journal of Partial Differential Equations 2022年第4期35卷 344-359页

作者： YU Yanghai LI Jinlu YIN Xiuwei School of Mathematics and Statistics Anhui Normal UniversityWuhu 241002China School of Mathematics and Computer Sciences Gannan Normal UniversityGanzhou 341000China

this paper,we consider the Cauchy problem of 3D tropical climate model with zero thermal diffusion.Firstly,we establish the global regularity for this system with fractional diffusionα=β=5/4.Secondly,by adding only ... 详细信息

关键词： tropical climate model zero thermal diffusion global well-posedness

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Global Regularity of 2D Leray-Alpha Regularized tropical climate models

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Journal of Partial Differential Equations 2020年第3期33卷 208-221页

作者： ZHANG Ying YUAN Baoquan School of Mathematics and Information Science Henan Polytechnic UniversityJiaozuo 454000China

In this paper,we establish the global regularity of 2D leray-alpha regularized tropical climate models.The global strong solution to the system with a half Laplacian of the first baroclinic model of velocity(Av)and th... 详细信息

关键词： tropical climate model Leray-alpha model global regularity

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