Differentiating the first with respect to y , the second with respect to x and subtracting the resulting equations will eliminate pressure and any conservative force. For incompressible flow, defining the stream function ψ ψ through u x = ∂ ∂ ψ ψ ∂ ∂ y ; u y = − − ∂ ∂ ψ ψ ∂ ∂ x results in mass continuity being unconditionally satisfied (given the stream function is continuous), and then incompressible Newtonian 2D momentum and mass conservation condense into one equation: ∂ ∂ ∂ ∂ t ( ∇ ∇ 2 ψ ψ ) + ∂ ∂ ψ ψ ∂ ∂ y ∂ ∂ ∂ ∂ x ( ∇ ∇ 2 ψ ψ ) − − ∂ ∂ ψ ψ ∂ ∂ x ∂ ∂ ∂ ∂ y ( ∇ ∇ 2 ψ ψ ) = ν ν ∇ ∇ 4 ψ ψ