  It is a well-known fact that the gravitational effect of dark matter in
galaxies is only noticeable when the orbital accelerations drop below $a_0
\simeq 2\times 10^{-8}$ cm s$^{-1}$ (Milgrom's Law). This peculiarity of the
dynamic behaviour of galaxies was initially ascribed to a modification of
Newtonian dynamics (MOND theory) and, consequently, it was used as an argument
to criticize the dark matter hypothesis. In our model, warm dark matter is
composed by collisionless Vlasov particles with a primordial typical velocity
$\simeq 330$ km s$^{-1}$ and, consequently, they evaporated from galactic cores
and reorganized in halos with a cusp at a finite distance from the galactic
center (in contrast with Cold Dark Matter simulations which predict a cusp at
the center of galaxies). This is confirmed by mean-field N-body simulations of
the self-gravitating Vlasov dark matter particles in the potential well of the
baryonic core. The rest mass of these particles, $\mu$, is determined from a
kinetic theory of the early universe with a cosmological constant. We find that
$\mu$ is in the range of a few keV. This result makes sterile neutrinos the
best suited candidates for the main component of dark matter.
