  Recent structure models of Jupiter that match Juno gravity data suggest that
the planet harbours an extended region in its deep interior that is enriched in
heavy elements, a so-called dilute/fuzzy core. This finding raises the question
of what possible formation pathways would lead to such a structure. We model
Jupiter's formation and long-term evolution, starting at late-stage formation
before runaway gas accretion. The formation scenarios we consider include both
primordial composition gradients, as well as gradients that are built as
proto-Jupiter rapidly acquires its gaseous envelope. We then follow Jupiter's
evolution as it cools down and contracts, with a particular focus on the energy
and material transport in the interior. We find that none of the scenarios we
consider lead to a fuzzy core that is compatible with interior structure
models. In all the cases, most of Jupiter's envelope becomes convective and
fully mixed after at most a few million years. This is true even when we
consider a case where the gas accretion leads to a cold planet, and large
amounts of heavy elements are accreted. It is therefore concluded that it is
very challenging to explain Jupiter's dilute core from standard formation
models. We suggest that future work should consider more complex formation
pathways as well as the modelling of additional physical processes that could
lead to Jupiter's current-state internal structure.
