The maximum principle for the equation of continuity of compressible media

The maximum principle is established for classical and generalized solution ρ (x, t) for the problem\r\n∂ρ∂t+div(ρv)=0,x∈Ω⊂Rn,t>0 (1)\r\nρ(x,t)|t=0=ρ0(x),(v,n)|∂Ω=0 (2)\r\nfor a given flow v(x,t), where n is the unit normal to ∂Ω, c.f. Maslennikova and Bogovskii (1994).