The first equation is the Euler momentum equation with uniform density (for this equation it could also not be constant in time). By expanding the material derivative, the equations become: { ∂ ∂ u ∂ ∂ t + ( u ⋅ ⋅ ∇ ∇ ) u = − − ∇ ∇ w + g ∇ ∇ ⋅ ⋅ u = 0