  Ring-shaped superfluids with weak links provide a perfect environment for
studying persistent currents and dynamic stirring protocols. Here, we
investigate the effects of a weak-link system on dipolar supersolids. By
calculating the ground state energy at fixed angular momenta, we find that
metastable persistent currents may exist in the supersolid phase near the
superfluid transition point. When stirring the weak link rapidly enough, we
show that vortices can enter the supersolid. These vortex entries cause phase
slips, emitting solitonic excitations that interfere with the crystalline
structure of the supersolid, leading to a continuous melting and
recrystallization of the droplets. Finally, we examine the release of
vortex-carrying supersolids from the trap, observing that the released density
exhibits a discrete structure associated with the density modulation and a
central hole resulting from the vortex core.
