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Global solvability of the problem on the motion of two fluids without surface tension

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Abstract

Unsteady motion of viscous incompressible fluids is considered in a bounded domain. The liquids are separated by an unknown interface on which the surface tension is neglected. This motion is governed by an interface problem for the Navier-Stokes system. First, a local existence theorem is established for the problem in Hölder classes of functions. The proof is based on the solvability of a model problem for the Stokes system with a plane interface, which was obtained earlier. Next, for a small initial velocity vector field and small mass forces, we prove the existence of a unique smooth solution to the problem on an infinite time interval. Bibliography: 7 titles.

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Authors and Affiliations

  1. Institute of Mechanical Engineering Problems, Russian Academy of Sciences, St.Petersburg, Russia

    I. V. Denisova

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  1. I. V. Denisova
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Correspondence to I. V. Denisova.

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Published in Zapiski Nauchnykh Seminarov POMI, Vol. 348, 2007, pp. 19–39.

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Denisova, I.V. Global solvability of the problem on the motion of two fluids without surface tension. J Math Sci 152, 625–637 (2008). https://doi.org/10.1007/s10958-008-9096-1

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  • DOI: https://doi.org/10.1007/s10958-008-9096-1

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