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.