Denisova, I. V.

Linear stability problem for a rotating two-phase liquid mass

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

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

    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.

Russian, 33 pp.

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