Nonlinear waves in a viscous horizontal film in the presence of an electric field

In this work, we consider the influence of non-conservative forces in the propagation of weakly nonlinear waves on the surface of a shallow viscous perfectly conducting liquid layer stressed by a normal electric field. We introduce the viscous losses at the bottom solving the boundary layer equations for the velocity. We derive an integro-differential equation for the deflection of the interface. To prevent the decay of the waves, we discuss the possibility of sustaining them through an external input of electrical energy. For an ohmic liquid there appear tangential interfacial stresses that could pull the liquid. We perform an energy balance of the system and deduce the order of magnitude for the electric fields needed to maintain these waves.