Noise-sustained structures in the Kuramoto-Sivashinsky equation

Abstract
We investigate the interaction between external noise and spatial degrees of freedom for the Kuramoto-Sivashinsky (KS) equation with and without damping, a prototype equation which is known to show weak spatial turbulence and which arises in many areas including flame fronts, flow down an inclined plane, convection between insulating boundaries, etc. We show that the KS equation can be convectively unstable and can lead to noise-sustained structures.