We consider the properties of a relativistic Fermi gas. In particular we derive expressions for the flow velocities behind strong and weak shock waves. We use these results to consider the validity of attempts to bound neutrino-neutrino cross sections from the supernova SN1987A. Certain apporaches to such bounds appear to be invalid. We also apply this picture to a recently proposed scenario for galaxy formation in the presence of light neutrinos with large cross sections.