From:
ρ ( ∂u/∂t + (u · ∇)u ) = -∇p + μ ∇² u
lim_{t → t_c} ||u(x, t)|| = ∞ ⟺ ∇ → ∞
u ↦ Φ = ∏_{i=1}^{3} C_i
∇ ↦ Φ⁻¹
S = Φ + Φ⁻¹
Φ · Φ⁻¹ = 1
Re = ρ u L / μ ∝ Φ
Eu = Δp / (ρ u²) ∝ Φ⁻¹
Re · Eu = ( ρ u L / μ ) · ( Δp / (ρ u²) ) = Δp L / (μ u)
Δp L / (μ u) ≡ Φ · Φ⁻¹ = 1
u = Δp L / μ
lim_{Φ → ∞} Eu = 0 ⟹ Δp → 0
lim_{Φ → ∞} u = lim_{Δp → 0} (Δp L / μ) = 0
u ∈ [0, u_max] ⟹ u ≠ ∞
∴ lim_{t → t_c} ||u(x, t)|| ≠ ∞
