We will describe the derivation of a nonlinear evolution equation that describes space-time self-organization at the free surface of a solid target undergoing irradiation by an energetic ion beam. Under this type of driving, for many materials the outermost surface layer of the target responds as a highly viscous fluid, displaying formation of nanoscale ripples in macroscopic time scales. In spite of the irrelevance of gravity at these small distances, the weakly nonlinear limit of the equation resembles the well known description of a macroscopic incompressible viscous thin film flowing down an incline, which is a paradigmatic instance of free surface flow systems for which the morphological instability responsible for pattern formation is controlled by inertial effects. The predictive power of the evolution equation for ion-beam surface nanopatterning underscores nonlinear effects that might have been expected to be of a secondary importance in such a nanoscopic-scale, Stokes-flow system. The content of this talk is joint work with Mario Castro (Universidad Pontificia Comillas) and Javier Muñoz-García (UC3M).