References
A. L. Frenkel, A. J. Babchin, B. J. Levich, et al., “Annular flows can keep unstable films from breakup: nonlinear saturation of capillary instability,”J. Colloid Interface Sci.,115, No. 1, 225–233 (1987).
D. T. Papageorgiou, C. Maldarelli, and D. S. Rumschitzki, “Nonlinear interfacial stability of coreannular film flows,”Phys. Fluids A,2, No. 3, 340–352 (1990).
E. Georgiou, C. Maldarelli, D. T. Papageorgiou, and D. S. Rumschitzki, “An asymptotic theory for the linear stability of a core-annular flow in the thin annular limit,”J. Fluid Mech.,243, 653–677 (1992).
P. S. Hammond, “Nonlinear adjustment of a thin annular film of viscous fluid surrounding a thread of another within a circular cylindrical pipe,”J. Fluid Mech.,137, 363–384 (1983).
V. V. Pukhnachyov,Viscous Fluid Flow with Free Boundaries [in Russian], Izd. Novosibirsk Univ., Novosibirsk (1989).
T. Kawahara, “Formation of saturated solutions in a nonlinear dispersive system with instability and dissipation,”Phys. Rev. Lett.,51, No. 5, 381–383 (1983).
G. I. Sivashinsky and D. M. Michelson, “On irregular wavy flow of a liquid film down a vertical plane,”Prog. Theor. Phys.,63, 2112–2114 (1980).
D. M. Michelson and G. I. Sivashinsky, “Nonlinear analysis of hydrodynamic instability in laminar flames. 2. Numerical experiments,”Acta Astronaut.,4, 1207–1221 (1977).
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Computing Center, Siberian Division, Russian Academy of Sciences, Krasnoyarsk 660036. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 38, No. 1, pp. 178–186, January–February, 1997.
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Zakhvatayev, V.E. Some weakly nonlinear amplitude equations describing the behavior of a thin layer in a two-phase flow of viscous heat-conducting liquids along a cylinder. J Appl Mech Tech Phys 38, 161–168 (1997). https://doi.org/10.1007/BF02468288
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DOI: https://doi.org/10.1007/BF02468288