  We present simulation results of the vortex dynamics in a trapped
Bose-Einstein condensate in the presence of a rotating optical lattice.
Changing the potential amplitude and the relative rotation frequency between
the condensate and the optical lattice, we find a rich variety of dynamical
phases of vortices. The onset of these different phases is described by the
force balance of a driving force, a pinning force and vortex-vortex
interactions. In particular, when the optical lattice rotates faster than the
condensate, an incommensurate effect leads to a vortex liquid phase supported
by the competition between the driving force and the dissipation.
