Note finally that this last equation can be derived by solving the three-dimensional Navier–Stokes equations for the equilibrium situation where u = v = ∂ ∂ p ∂ ∂ x = ∂ ∂ p ∂ ∂ y = 0 Then the only non-trivial equation is the z -equation, which now reads ∂ ∂ p ∂ ∂ z + ρ ρ g = 0 Thus, hydrostatic balance can be regarded as a particularly simple equilibrium solution of the Navier–Stokes equations.