Geodesic
Evolution of compressible and incompressible fluids separated by a closed interface
Irina V. Denisova1
1Russian Acadademy of Sciences, St. Petersburg, Russian Federation
Interfaces and free boundaries, Tome 2 (2000) no. 3, pp. 283-312

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DOI

This work solves the problem governing the simultaneous motion of two viscous liquids of different kinds: compressible and incompressible. The boundary between the fluids is considered as an unknown (free) interface where the surface tension is taken into account. Although the fluids occupy the whole space 3, one of them should have a finite volume. Local (in time) unique solvability of this problem is obtained in the Sobolev-Slobodetski[inodot]spaces of functions. Estimates of the solution of a model problem for the Stokes equations are considered in detail, the interface between the fluids being a plane. The Schauder method is used to study a linear problem with a compact boundary. The passage to the nonlinear problem is made by successive approximations.
DOI : 10.4171/ifb/21
Classification : 46-XX, 60-XX
Mots-clés : Free boundary problem, Navier-Stokes equations, two immiscible fluids

Irina V. Denisova  1

1 Russian Acadademy of Sciences, St. Petersburg, Russian Federation 
Irina V. Denisova. Evolution of compressible and incompressible fluids separated by a closed interface. Interfaces and free boundaries, Tome 2 (2000) no. 3, pp. 283-312. doi: 10.4171/ifb/21
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     title = {Evolution of compressible and incompressible fluids separated by a closed interface},
     journal = {Interfaces and free boundaries},
     pages = {283--312},
     year = {2000},
     volume = {2},
     number = {3},
     doi = {10.4171/ifb/21},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/21/}
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