  In order to reproduce the low mass end of the stellar mass function, most
current models of galaxy evolution invoke very efficient supernova feedback.
This solution seems to suffer from several shortcomings however, like
predicting too little star formation in low mass galaxies at z=0. In this work,
we explore modifications to the star formation (SF) law as an alternative
solution to achieve a match to the stellar mass function. This is done by
applying semi-analytic models based on De Lucia & Blaizot, but with varying SF
laws, to the Millennium and Millennium-II simulations, within the formalism
developed by Neistein & Weinmann. Our best model includes lower SF efficiencies
than predicted by the Kennicutt-Schmidt law at low stellar masses, no sharp
threshold of cold gas mass for SF, and a SF law that is independent of cosmic
time. These simple modifications result in a model that is more successful than
current standard models in reproducing various properties of galaxies less
massive than 10^{10}Msun. The improvements include a good match to the observed
auto-correlation function of galaxies, an evolution of the stellar mass
function from z=3 to z=0 similar to observations, and a better agreement with
observed specific star formation rates. However, our modifications also lead to
a dramatic over-prediction of the cold mass content of galaxies. This shows
that finding a successful model may require fine-tuning of both star formation
and supernovae feedback, as well as improvements on gas cooling, or perhaps the
inclusion of a yet unknown process which efficiently heats or expels gas at
high redshifts.
