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Evolution of a Closed Interface between Two Liquids of Different Types

  • Irina V. Denisova
Conference paper
Part of the Progress in Mathematics book series (PM, volume 202)

Abstract

We study a free boundary problem governing the motion of two immiscible viscous capillary fluids. The fluids occupy the whole space R3 but one of them should have a finite volume. Every liquid may be of both types: compressible and incompressible.

Local (with respect to time) unique solvability of the problem is obtained in the Sobolev-Slobodetskii spaces. After the passage to Lagrangian coordinates, one obtains a nonlinear, noncoercive initial boundary-value problem the proof of the existence theorem for which is based on the method of successive approximations and on an explicit solution of a model linear problem with a plane interface between the liquids.

Some restrictions to the fluid viscosities appear in the case when at least, one of the liquids is compressible.

Keywords

Incompressible Fluid Plane Interface Free Boundary Problem Finite Time Interval Unique Solvability 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Basel AG 2001

Authors and Affiliations

  • Irina V. Denisova
    • 1
  1. 1.Institute of Mechanical Engineering ProblemsRussian Academy of SciencesSt. PetersburgRussia

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