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Dynamics of the interface between two immiscible liquids with nearly equal densities under gravity

Published online by Cambridge University Press:  28 November 2002

V. G. DANILOV  and
G. A. OMEL'YANOV
V. G. DANILOV
Affiliation:
Moscow Technical University of Communication and Informatics, Moscow, Russia email: pm@miem.edu.ru
G. A. OMEL'YANOV
Affiliation:
Moscow State Institute of Electronics and Mathematics, Moscow, Russia email: pm@miem.edu.ru
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Abstract

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We consider the two-dimensional Rayleigh–Taylor problem for the dynamics of the free interface Γ between two layers of immiscible viscous liquids. For a slow flow model (which corresponds to the case of a small relative jump of density) and under sufficiently wide assumptions on the geometry of Γ, we analyze the time dynamics of Γ. In particular, we prove that its increase in time t is bounded by an exponential function with exponent independent of Γ.

Type
Research Article
Information
European Journal of Applied Mathematics , Volume 13 , Issue 5 , October 2002 , pp. 497 - 516
Copyright
2002 Cambridge University Press