Collisionless dark-matter Vlasov equation
= Collisionless dark-matter Vlasov equation
{c}
{wiki=Vlasov_equation}
For comoving position $\mathbf x$, canonical momentum $\mathbf p=am\mathbf x'$, and Newtonian potential $\phi$, the dark-matter phase-space density obeys
$$
\partial_\eta f+\frac{\mathbf p}{am}\mathbin\cdot\nabla_xf-am\nabla\phi\mathbin\cdot\nabla_pf=0.
$$