  We discuss dissipative dynamics of a vortex state in a trapped Bose-condensed
gas at finite temperature and draw a scenario of decay of this state in a
static trap. The interaction of the vortex with the thermal cloud transfers
energy from the vortex to the cloud and induces the motion of the vortex core
to the border of the condensate. Once the vortex reaches the border, it
immediately decays through the creation of excitations. We calculate the
characteristic life-time of a vortex state and address the question of how the
dissipative dynamics of vortices can be studied experimentally.
