TITLE:
Global Well-Posedness of the Fractional Tropical Climate Model
AUTHORS:
Meiqi Hu
KEYWORDS:
Tropical Climate Model, Fractional Diffusion, Global Existence
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.12 No.3,
March
25,
2024
ABSTRACT: 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.