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.