Rotation Problem for a Two-Phase Drop

被引：2

作者：

Denisova, I., V ^{[1
]}

Solonnikov, V. A. ^{[2
]}

机构：

[1] Russian Acad Sci, Inst Problems Mech Engn, 61 Bolshoy Av, St Petersburg 199178, Russia

[2] Russian Acad Sci, St Petersburg Dept VA Steklov Inst Math, 27 Fontanka, St Petersburg 191023, Russia

来源：

JOURNAL OF MATHEMATICAL FLUID MECHANICS | 2022年 / 24卷 / 02期

关键词：

Two-phase problem; Viscous incompressible fluids; Interface problem; Navier-Stokes system; Sobolev-Slobodetskii spaces; EQUILIBRIUM; STABILITY; FIGURES;

D O I：

10.1007/s00021-022-00662-x

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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 -> infinity, the motion of the drop going over to the rotation of the liquid mass as a rigid body.

引用

页数：26