  A new method is presented to prove finiteness of the fractal and Hausdorff
dimensions of the global attractor for the strong solutions to the 3D Primitive
Equations with viscosity, which is applicable to even more general situations
than the recent result of [7] in the sense that it removes all extra technical
conditions imposed by previous analyses. More specifically, for finiteness of
the dimensions of the global attractor, we only need the heat source $Q\in L^2$
which is exactly the condition for the existence of global strong solutions and
the existence of the global attractor of these solutions; while the best
existing result, which was obtained very recently in [7], still needs the extra
condition that $\partial_z Q\in L^2 $ for finiteness of the dimensions of the
global attractor. Moreover, the new method can be applied to cases with more
complicated boundary conditions which present essential difficulties for
previous methods.
