Inertial manifold of the atmospheric equations

For a class of nonlinear evolution equations, their global attractors are s tudied and the existence of their inertial manifolds is discussed using the truncated method. Then, on the basis of the properties of operators of the atmospheric equations, ii is proved that the operator equation of the atmo spheric motion with dissipation and external forcing belongs to the class o f nonlinear evolution equations. Therefore, it is known that there exists a n inertial manifold of the atmospheric equations ii the spectral gap condit ion for the dissipation operator is satisfied. These results furnish a basi s for further studying the dynamical properties of global attractor of the atmospheric equations and for designing better numerical scheme.