Spectral analysis and global well-posedness for a viscous tropical climate model with only a damp term. (February 2018) - Ma, Caochuan; Wan, Renhui
Abstract: Tropical climate model derived by Frierson–Majda–Pauluis in Frierson et al. (2004) has been studied by many works (see, e.g., Li and Titi (2016); Li and Titi (2016); Wan (2016)). In this paper, we consider the Cauchy problem for the viscous tropical climate model with only a damp term and obtain the global well-posedness for the small data. The estimate of ∫ 0 t ‖ ∇θ‖ L ∞ 2 d τ is the main difficulty. To achieve our goal, we need using the spectral analysis to the system and constructing a new energy estimate of u in Besov space.