Global Attractors for the Three-Dimensional Viscous Primitive Equations of Large-Scale Atmosphere in Log-Pressure Coordinate

Abstract

We will first prove the existence of $(V,V)$- and $(V,H^2)$-absorbing sets for the three-dimensional primitive equations of large-scale atmosphere in log-pressure coordinate and then prove the existence of $(V,H^3)$-absorbing set by the use of the elliptic regularity theory. Finally, we obtain the existence of $(V,V)$- and $(V,H^2)$-global attractors for the three-dimensional viscous primitive equations of large-scale atmosphere in log-pressure coordinate by using the Sobolev compactness embedding theory.