UNIVERSAL PROPERTIES OF THE 2-DIMENSIONAL KURAMOTO-SIVASHINSKY EQUATION

We investigate the properties of the Kuramoto-Sivashinsky equation in two spatial dimensions. We show by an explicit, numerical, coarse-grai ning procedure that its long-wavelength properties are described by a stochastic, partial differential equation of the Kardar-Parisi-Zhang t ype. From the computed parameters in our effective, stochastic equatio n we argue that the length and time scales over which the correlation functions cross over from linear diffusive to those of the full nonlin ear equation are very large. The behavior of the three-dimensional equ ation is also discussed.