  Nucleation of vortices in rotating superfluid by spin-up and rapid thermal
quench is discussed in the framework of the time-dependent Ginzburg--Landau
equation (TDGLE). An analysis of the instability in inhomogeneous
rotationally-invariant system results in the expression for the critical
rotational velocity. A stability analysis of multicharged vortices is
presented. It is shown that they are very long-living objects with lifetime
inversely proportional to the dissipation rate. It was found by numerical and
analytical solution of the TDGLE that vortex nucleation by rapid thermal quench
in the presence of superflow is dominated by a transverse instability of the
moving normal-superfluid interface.
