Instability and reformation of regular waves in falling film of a viscous liquid. (English. Russian original) Zbl 1014.76023

Sisoev, G. M.; Shkadov, V. Ya.

Mosc. Univ. Mech. Bull. 55, No. 4, 19-23 (2000); translation from Vestn. Mosk. Univ., Ser. I 2000, No. 4, 44-48 (2000).

The paper deals with the system of evolutionary equations in the form \(\frac{\partial h}{\partial t} +\frac{\partial q}{\partial x} = 0,\) \(\frac{\partial q}{\partial t} + \frac 65 \frac{\partial}{\partial x}\big(\frac 1{5\delta}\big) = \frac 1{5\delta}\big(h \frac{\partial^3 h}{\partial x^3} + h - \frac{q}{h^2}\big)\) which was studied earlier in [V. Ya. Shkadov, Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza 1, 43-50 (1967)]. The authors show that attractive properties of dominating waves are presented also in the case when the initial data are chosen in a small neighborhood of other regular waves.

Reviewer: V. I. Guljaev (Kyïv)

MSC:

76E17	Interfacial stability and instability in hydrodynamic stability
76M22	Spectral methods applied to problems in fluid mechanics
76D99	Incompressible viscous fluids

Keywords:

nonlinear regular wave solutions; instability; two-parameter manifold of solutions; attractor; finite Fourier series; Galerkin method; pseudospectral method; eigenvalue problem; falling film; viscous liquid; attractor of dominating waves; evolutionary equations