  We investigate baryogenesis in the $\nu$MSM (neutrino Minimal Standard
Model), which is the MSM extended by three right-handed neutrinos with masses
below the electroweak scale. The baryon asymmetry of the universe can be
generated by the mechanism via flavor oscillation of right-handed (sterile)
neutrinos which are responsible to masses of active neutrinos confirmed by
various experiments. We present the kinetic equations for the matrix of
densities of leptons which describe the generation of asymmetries. Especially,
the momentum dependence of the matrix of densities is taken into account. By
solving these equations numerically, it is found that the momentum distribution
is significantly distorted from the equilibrium one, since the production for
the modes with lower momenta $k \ll T$ ($T$ is the temperature of the universe)
is enhanced, while suppressed for higher modes. As a result, the most important
mode for the yields of sterile neutrinos as well as the baryon asymmetry is $k
\simeq 2 T$, which is smaller than < k > inferred from the thermal average. The
comparison with the previous works is also discussed.
