[Author]
 Denisova, I. V.

[Title]
 Linear stability problem for a rotating two-phase liquid mass

[AMS Subj-class]
 35Q30 Navier-Stokes equations
 76T06 Liquid-liquid two component flows
 76D05 Navier-Stokes equations for incompressible viscous fluids
 76D06 Statistical solutions of Navier-Stokes and related equations
 35R35 Free boundary problems for PDEs
 76D03 Existence, uniqueness, and regularity theory for incompressible viscous fluids

[Keywords]
 two-phase problem, viscous compressible and incompressible fluids, free boundary
 and interface problems, Navier--Stokes system, Sobolev--Slobodetskii spaces

[Abstract]
 The existence of a solution to the linearized problem of the rotation of a viscous
 two-phase drop consisting of compressible and incompressible fluids is proved.
 The inner fluid is the incompressible one. It is bounded by a closed, unknown
 surface that does not intersect the outer free boundary. The compressible fluid
 is barotropic. Surface tension forces act on both boundaries. It is assumed that
 the angular velocity is small, and the drop shape is close to a two-layer
 equilibrium figure. 
 A theorem on the global (in time) solvability of the problem is obtained in
 Sobolev--Slobodetski\v{\i} spaces.

[Comments]
 Russian, 33 pp.

[Contact e-mail]
 denisovairinavlad@gmail.com