Almost Periodic Passive Tracer Dispersion

The authors investigate the impact of external sources on the pattern formation of concentration profiles of passive tracers in a two-dimensional shear flow. By using the pullback attractor technique for the associated nonautonomous dynamical system, it is shown that a unique time-almost periodic concentration profile exists for time-almost periodic external source.Comment: latex fil

Asymptotic Dynamical Difference between the Nonlocal and Local Swift-Hohenberg Models

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