Geodesic
An asymptotic study of three-layered creeping flow and some geophysical applications
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 4 (2011), pp. 107-115

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The nonlinear model based on the long-wave approximation of the Navier–Stokes equations is developed to study the free-surface three-layered creeping flow. An asymptotic study of the governing equations reveals two different modes of evolution at a short and long time. The relation between layers' boundaries is obtained that is independent of a pre-history of the flow. The obtained results are applied to study a behavior of the deep interface beneath the large-scale lunar basin under the variation of geometrical and physical model's parameters.
Keywords: multi-layered flow, long-wave approximation, lubrication theory, nonlinear diffusion, ring basins. 
@article{VUU_2011_4_a8,
     author = {V. V. Pak},
     title = {An asymptotic study of three-layered creeping flow and some geophysical applications},
     journal = {Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹ\^uternye nauki},
     pages = {107--115},
     publisher = {mathdoc},
     number = {4},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VUU_2011_4_a8/}
}
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V. V. Pak. An asymptotic study of three-layered creeping flow and some geophysical applications. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 4 (2011), pp. 107-115. http://geodesic.mathdoc.fr/item/VUU_2011_4_a8/