  We investigate the rotational evolution of solar-like stars with a focus on
the internal angular momentum transport processes. The double zone model, in
which the star's radiative core and convective envelope are assumed to rotate
as solid bodies, is used to test simple relationships between the core-envelope
coupling timescale, tau_c, and rotational properties, like the envelope angular
velocity or the differential rotation at the core-envelope interface. The trial
relationships are tested by fitting the model parameters to available
observations via a Monte Carlo Markov Chain method. The synthetic distributions
are tested for compatibility with their observational counterparts by means of
the standard Kolmogorov-Smirnov (KS) test. A power-law dependence of tau_c on
the inner differential rotation leads to a more satisfactory agreement with
observations than a two-value prescription for tau_c, which would imply a
dichotomy between the initially slow (P_rot > 3 d) and fast (P_rot < 3 d)
rotators. However, we find it impossible to reconcile the high fraction of fast
rotators in alpha Per with the rotation period distributions in stellar systems
at earlier and later evolutionary stages. This could be explained by local
environmental effects (e.g. early removal of circumstellar discs due to UV
radiation and winds from nearby high-mass stars) or by observational biases.
The low KS probability that the synthetic and observed distributions are not
incompatible, found in some cases, may be due to over-simplified assumptions of
the double zone model, but the large relative uncertainties in the age
determination of very young clusters and associations are expected to play a
relevant role. Other possible limitations and uncertainties are discussed.
