Global attractor of the three-dimensional primitive equations of large-scale ocean and atmosphere dynamics

The objective of this paper is to study the existence of a global attractor in for the three-dimensional autonomous primitive equations of large-scale ocean and atmosphere dynamics. According to the regularity results for the Stokes-type system in cylinder-type domains established by Ziane (Appl Anal 58(3-4):263-292, 1995), we can only obtain the existence of an absorbing set in such that the compactness of the semigroup in cannot be proved by the Sobolev compactness embedding theorem. Therefore, in order to obtain the existence of a global attractor in we carry out some a priori estimates of strong solutions to establish the asymptotical compactness of the semigroup in by asymptotic a priori estimate.