The continuity equation describes how the density changes with time. It can be found by integration of the Vlasov equation over the entire velocity space. ∫ ∫ d f d t d 3 v = ∫ ∫ ( ∂ ∂ ∂ ∂ t f + ( v ⋅ ⋅ ∇ ∇ r ) f + ( a ⋅ ⋅ ∇ ∇ v ) f ) d 3 v = 0