  We present an experimental study of the flow dynamics of a lamellar phase
sheared in the Couette geometry. High-frequency ultrasonic pulses at 36 MHz are
used to measure time-resolved velocity profiles. Oscillations of the viscosity
occur in the vicinity of a shear-induced transition between a high-viscosity
disordered fluid and a low-viscosity ordered fluid. The phase coexistence shows
up as shear bands on the velocity profiles. We show that the dynamics of the
rheological data result from two different processes: (i) fluctuations of slip
velocities at the two walls and (ii) flow dynamics in the bulk of the lamellar
phase. The bulk dynamics are shown to be related to the displacement of the
interface between the two differently sheared regions in the gap of the Couette
cell. Two different dynamical regimes are investigated under applied shear
stress: one of small amplitude oscillations of the viscosity
($\delta\eta/\eta\simeq 3$%) and one of large oscillations
($\delta\eta/\eta\simeq 25$%). A phenomenological model is proposed that may
account for the observed spatio-temporal dynamics
