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Rotation Problem for a Two-Phase Drop

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Abstract

The paper deals with the stability of a uniformly rotating finite mass consisting of two immiscible viscous incompressible fluids with unknown interface and exterior free boundary. Capillary forces act on both surfaces. The proof of stability is based on the analysis of an evolutionary problem for small perturbations of the equilibrium state of a rotating two-phase fluid. It is proved that for small initial data and small angular velocity, as well as the positivity of the second variation of energy functional, the perturbation of the axisymmetric equilibrium figure exponentially tends to zero as \(t\rightarrow \infty \), the motion of the drop going over to the rotation of the liquid mass as a rigid body.

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Authors and Affiliations

  1. Institute for Problems in Mechanical Engineering, Russian Academy of Sciences, 61 Bol’shoy av., V.O., St. Petersburg, Russia, 199178

    I. V. Denisova

  2. St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences, 27 Fontanka, St. Petersburg, Russia, 191023

    V. A. Solonnikov

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  1. I. V. Denisova
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  2. V. A. Solonnikov
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Correspondence to I. V. Denisova.

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Communicated by T. Ozawa.

Dedicated to the 70th anniversary of Professor Yoshihiro Shibata.

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This article is part of the topical collection “Yoshihiro Shibata” edited by Tohru Ozawa. This research has been partially supported by the grant no. 20-01-00397 of the Russian Foundation of Basic Research.

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Denisova, I.V., Solonnikov, V.A. Rotation Problem for a Two-Phase Drop. J. Math. Fluid Mech. 24, 40 (2022). https://doi.org/10.1007/s00021-022-00662-x

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