A tropical atmosphere model with moisture: global well-posedness and relaxation limit. (1st August 2016)

• Record Type: Journal Article
• Authors: Li, Jinkai; Titi, Edriss S
• Is Part Of: Nonlinearity. Volume 29:Number 9(2016:Sep.)
• Page Start: 2674
• Page End: 2714
• Publication Date: 2016-08-01
• Subjects: tropical–extratropical interactions -- atmosphere with moisture -- primitive equations -- relaxation limit -- variational inequality; 35M86 -- 35Q35 -- 76D03 -- 86A10; Nonlinear theories -- Periodicals; Mathematical analysis -- Periodicals; Mathematical analysis; Nonlinear theories; Periodicals; 515
• DOI: 10.1088/0951-7715/29/9/2674
• Languages: English
• ISSNs: 0951-7715

Abstract

Abstract: In this paper, we consider a nonlinear interaction system between the barotropic mode and the first baroclinic mode of the tropical atmosphere with moisture, which was derived in Frierson et al (2004 Commum. Math. Sci .2 591–626 ). We establish the global existence and uniqueness of strong solutions to this system, with initial data in H 1, for each fixed convective adjustment relaxation time parameter ε > 0 . Moreover, if the initial data possess slightly more regularity than H 1, then the unique strong solution depends continuously on the initial data. Furthermore, by establishing several appropriate ε -independent estimates, we prove that the system converges to a limiting system as the relaxation time parameter ε tends to zero, with a convergence rate of the order O ( ε ) . Moreover, the limiting system has a unique global strong solution for any initial data in H 1 and such a unique strong solution depends continuously on the initial data if the initial data posses slightly more regularity than H 1 . Notably, this solves theviscous version of an open problem proposed in the above mentioned paper of Frierson, Majda and Pauluis.