  We are concerned with global-in-time existence and uniqueness results for
models of pressureless gases that come up in the description of phenomena in
astrophysics or collective behavior. The initial data are rough: in particular,
the density is only bounded. Our results are based on interpolation and
parabolic maximal regularity, where Lorentz spaces play a key role. We
establish a novel maximal regularity estimate for parabolic systems in
$L_{q,r}(0,T;L_p(\Omega))$ spaces.
