Kardar-Parisi-Zhang asymptotics for the two-dimensional noisy   Kuramoto-Sivashinsky equation
  We study numerically the Kuramoto-Sivashinsky (KS) equation forced by external white noise in two space dimensions, that is a generic model for e.g. surface kinetic roughening in the presence of morphological instabilities. Large scale simulations using a pseudospectral numerical scheme allow us to retrieve Kardar-Parisi-Zhang (KPZ) scaling as the asymptotic state of the system, as in the 1D case. However, this is only the case for sufficiently large values of the coupling and/or system size, so that previous conclusions on non-KPZ asymptotics are demonstrated as finite size effects. Crossover effects are comparatively stronger for the 2D case than for the 1D system. 
Matteo Nicoli, Edoardo Vivo, and Rodolfo Cuerno
cond-mat.stat-mech cond-mat.dis-nn cond-mat.mtrl-sci nlin.AO