Passive Tracer Dispersion with Random or Periodic Source

In this paper, the author investigates the impact of external sources on the pattern formation and long-time behavior of concentration profiles of passive tracers in a two-dimensional shear flow. It is shown that a time-periodic concentration profile exists for time-periodic external source, while for random source, the distribution functions of all concentration profiles weakly converge to a unique invariant measure (like a stationary state in deterministic systems) as time goes to infinityComment: LaTeX file, 9 page

Almost Periodic Solutions and Global Attractors of Non-autonomous Navier-Stokes Equations

The article is devoted to the study of non-autonomous Navier-Stokes equations. First, the authors have proved that such systems admit compact global attractors. This problem is formulated and solved in the terms of general non-autonomous dynamical systems. Second, they have obtained conditions of convergence of non-autonomous Navier-Stokes equations. Third, a criterion for the existence of almost periodic (quasi periodic,almost automorphic, recurrent, pseudo recurrent) solutions of non-autonomous Navier-Stokes equations is given. Finally, the authors have derived a global averaging principle for non-autonomous Navier-Stokes equations.Comment: J. Dynamics and Diff. Eqns., in press, 200

Dynamics of a Nonlocal Kuramoto-Sivashinsky Equation

In this paper we study the effects of a ``nonlocal'' term on the global dynamics of the Kuramoto-Sivashinsky equation. We show that the equation possesses a ``family of maximal attractors'' parameterized by the mean value of the initial data. The dimension of the attractor is estimated as a function of the coefficient of the nonlocal term and the width of the periodic domain.Comment: Latex fil