Asymptotic dynamical difference between the nonlocal and local Swift-Hohenberg models

In this paper the difference in the asymptotic dynamics between the nonloca l and local two-dimensional Swift-Hohenberg models is investigated. It is s hown that the bounds for the dimensions of the global attractors for the no nlocal and local Swift-Hohenberg models differ by an absolute constant, whi ch depends only on the Rayleigh number, and upper and lower bounds of the k ernel of the nonlocal nonlinearity. Even when this kernel of the nonlocal o perator is a constant function, the dimension bounds of the global attracto rs still differ by an absolute constant depending on the Rayleigh number. ( C) 2000 American Institute of Physics. [S0022-2488(00)01204-4].