The boundedness of 2‐D liquid film flows on an inclined plane in the context of the
regularized Benney, u τ+ λ u 2 ux+[(μ u 6− ν u 3) ux] x+ σ {u 3 [u xx/(1+ ε2 ux 2) 3/2] x} x= 0,
and the Benney (ε= 0) equation are studied. Here u, x, τ are the rescaled film thickness, the
longitudinal coordinate, and time, respectively; λ, μ, and ν are non‐negative constants
determined at equilibrium; and ε is the parameter related to the film aspect ratio. For a
vertical plane (ν= 0) a critical curve λ= λ c (μ) has been found bifurcating from the point (λ …