Equilibrium Figures for a Rotating Compressible Capillary Two-Layer Liquid

Irina Vladimirovna Denisova () and Vsevolod Alexeevich Solonnikov
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Irina Vladimirovna Denisova: Institute for Problems in Mechanical Engineering, Russian Academy of Sciences, 61 Bol’shoy Av., V. O., St. Petersburg 199178, Russia
Vsevolod Alexeevich Solonnikov: St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences, 27 Fontanka, St. Petersburg 191023, Russia

Mathematics, 2023, vol. 12, issue 1, 1-15

Abstract: The paper proves the existence of a family of axisymmetric equilibrium figures as solutions of a stationary problem with unknown boundaries for the Navier–Stokes equations corresponding to the slow rotation of a viscous compressible two-layer liquid mass about some axis. It is assumed that the liquids are barotropic and capillary, and have different viscosities, the internal fluid being bounded by a closed surface. This interface does not intersect with the external boundary of the cloud. The proof is based on implicit function theorem and carried out in the Hölder spaces.

Keywords: equilibrium figures; viscous compressible two-layer fluid; capillary forces; interface problem for the Navier–Stokes system; the Hölder spaces (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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