Hydrodynamic description of neutrino gas

The system of neutrino-antineutrino $(\nu \bar{\nu })$ - plasma is considered taking into account their weak Fermi interaction. New fluid instabilities driven by strong neutrino flux in a plasma are found. The nonlinear stationary as well as nonstationary waves in the neutrino gas are discussed. It is shown that a bunch of neutrinos, drifting with a constant velocity across a homogeneous plasma, can also induce emission of lower energy neutrinos due to scattering, i.e. the decay of a heavy neutrino ${\nu }_H$ into a heavy and a light neutrino ${\nu }_L$ (${\nu }_H\to {\nu }_H{\nu }_L$) in a plasma. Furthermore we find that the neutrino production in stars does not lead in general to energy losses from the neutron stars.