Existence of the atmosphere attractor

The global asymptotic behavior of solutions for the equations of large scale atmospheric motion with the non-stationary external forcing is studied in the infinite dimensional Hilbert space. Based on the properties of operators of the equations, some energy inequalities and the uniqueness theorem of solutions are obtained. On the assumption that external forces are bounded, the exsitence of the global absorbing set and the atmosphere attractor is proved, and the characteristics of the decay of effect of initial field and the adjustment to the external forcing are revealed. The physical sense of the results is discussed and some ideas about climatic numerical forecast are elucidated Work supported by the State Key Research Project on Dynamics and Predictive Theory of the Climate.