Geodesic
The generalized statement of the problem of a two--phase liquid flow with continuously changing interface
Matematičeskoe modelirovanie, Tome 20 (2008) no. 3, pp. 3-8.

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In the paper the two-dimension problem of a two-phase immiscible liquid flow in the formulation of the incompressible Navier-Stokes equations with continuously changing interface is considered. For its definition during each moment of time is used so-called level set function. Besides discontinuous coefficients of kinematic viscosity and density in the formulation of a problem the effect of a surface tension is included. The generalized statement of a problem included conditions of the matching of the solution (in weak sense) on the common boundary between liquids is certain. 
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A. V. Rukavishnikov. The generalized statement of the problem of a two--phase liquid flow with continuously changing interface. Matematičeskoe modelirovanie, Tome 20 (2008) no. 3, pp. 3-8. http://geodesic.mathdoc.fr/item/MM_2008_20_3_a0/

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