Global Well-Posedness of the Fractional Tropical Climate Model

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.

Global Strong Solutions and Large-time Behavior of 2D Tropical Climate Model

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.

Global strong solution of 3D tropical climate model with damping

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 forα,β,γsatisfying one of the following three conditions:(1)α,β≥4;(2)7/2≤α<4,β≥(5α+7)/(2α),γ≥7/(2α−5);(3)3<α≤7/2,β,γ≥7/(2α−5).

Global Regularity of 2D Leray-Alpha Regularized Tropical Climate Models

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 thermal diffusion(△θ)or with only the dissipation of the barotropic mode(-Au)are obtained.

Global Well-Posedness for the 3D Tropical Climate Model without Thermal Diffusion

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 a damp term,we obtain the global well-posedness for small initial data.