Global well-posedness of strong solutions to a tropical climate model

Abstract

In this paper, we consider the Cauchy problem to the TROPIC CLIMATE MODEL derived by Frierson-Majda-Pauluis in [Comm. Math. Sci, Vol. 2 (2004)] which is a coupled system of the barotropic and the first baroclinic modes of the velocity and the typical midtropospheric temperature. The system considered in this paper has viscosities in the momentum equations, but no diffusivity in the temperature equation. We establish here the global well-posedness of strong solutions to this model. In proving the global existence of strong solutions, to overcome the difficulty caused by the absence of the diffusivity in the temperature equation, we introduce a new velocity $w$ (called the pseudo baroclinic velocity), which has more regularities than the original baroclinic mode of the velocity. An auxiliary function $\varphi$, which looks like the effective viscous flux for the compressible Navier-Stokes equations, is also introduced to obtain the $L^{\infty }$ bound of the temperature. Regarding the uniqueness, we use the idea of performing suitable energy estimates at level one order lower than the natural basic energy estimates for the system.

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• Local and Global Well-posedness of Strong Solutions to the 3D Primitive Equations with Vertical Eddy Diffusivity
• Global well-posedness of the 2D Boussinesq equations with vertical dissipation
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• On the uniqueness of weak solutions to the Ericksen-Leslie liquid crystal model in ${\mathbb{R}}^2$

Cited by in corpus (2)

• Global small solutions to a tropical climate model without thermal diffusion
• Multiple-scale analysis on the radiation within the coupled KdV equations