Abstract
The linear problem of the stability of plane-parallel flow with a free boundary was studied on the basis of the Navier--Stokes equations in [5-9]. The nonlinear problem was investigated in [10-14] within the framework of the equations of P. L. Kapitsa; the Korteweg--de Vries equation and equations similar to it were used in [15, 16] to describe the flow in a liquid film. Nonlinear flow conditions in a liquid film and nonlinear stability were studied in [17-20] on the basis of the Navier--Stokes equations in a long-wave approximation. In the two latter works the Landau constant was calculated using a modified Reynolds--Potter method [21] and a conclusion was drawn with respect to the absence of long-wave subcritical motions.
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