Spectral analysis and global well-posedness for a viscous tropical climate model with only a damp term. (February 2018)

• Record Type: Journal Article
• Authors: Ma, Caochuan; Wan, Renhui
• Is Part Of: Nonlinear analysis. Volume 39(2018)
• Page Start: 554
• Page End: 567
• Publication Date: 2018-02
• Subjects: Tropical climate model -- Global well-posedness -- Spectral analysis; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2017.08.004
• Languages: English
• ISSNs: 1468-1218

Abstract

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.