  We study a system of $ N $ trapped bosons in the Thomas-Fermi regime with an
interacting pair potential of the form $ g_N N^{3\beta-1} V(N^\beta x) $, for
some $ \beta\in(0,1/3) $ and $ g_N $ diverging as $ N \to \infty $. We prove
that there is complete Bose-Einstein condensation at the level of the ground
state and, furthermore, that, if $ \beta\in (0,1/6) $, condensation is
preserved by the time evolution.
