In this paper the difference in the asymptotic dynamics between the nonlocal
and local two-dimensional Swift-Hohenberg models is investigated. It is shown
that the bounds for the dimensions of the global attractors for the nonlocal
and local Swift-Hohenberg models differ by an absolute constant, which depends
only on the Rayleigh number, and upper and lower bounds of the kernel of the
nonlocal nonlinearity. Even when this kernel of the nonlocal operator is a
constant function, the dimension bounds of the global attractors still differ
by an absolute constant depending on the Rayleigh number.Comment: 13 pages, LaTex fil