Dynamics and delocalization transition for an interface driven by a uniform shear flow

We study the effect of a uniform shear how on an interface separating the t wo broken-symmetry ordered phases of a two-dimensional system with non-cons erved scalar order parameter. The interface, initially hat and perpendicula r to the flow, is distorted by the shear how. We show that there is a criti cal shear rate, gamma (c) proportional to 1/L-2 (where L is the system widt h perpendicular to the flow), below which the interface can sustain the she ar. In this regime the countermotion of the interface under its curvature b alances the shear how, and the stretched interface stabilizes into a time-i ndependent shape whose form we determine analytically. For gamma > gamma (c ) the interface acquires a non-zero velocity, whose profile is shown to rea ch a time-independent limit which we determine exactly. The analytical resu lts are checked by numerical integration of the equations of motion.