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**Tori of prescribed mean curvature and the rotating drop.**
*(English)*
Zbl 0581.76108

Variational methods for equilibrium problems of fluids, Meet. Trento/Italy 1983, Astérisque 118, 167-179 (1984).

[For the entire collection see Zbl 0544.00035.]

The author considers a fluid body rotating with constant angular velocity \(\omega\) and subject to surface tension. The gravity is either absent or has net effect. The mean curvature H of the surface of a fluid drop is given by (*) 2H\(=dv/dr+v/r\), where \(v=du/ds,\quad z=u(s),\quad r=r(s)\) are equations for a surface of revolution in cylindrical coordinates (r,\(\theta\),z) and s is an arclength parameter along the generating curve. The mathematical treatment of the rotating drop is based on the equation (*) and on the theory of elliptic integrals. It is shown that a large family of rotationally symmetric toroidal rotating drops exists and estimates on the possible rates of rotation are derived. The question of stability was not discussed.

The author considers a fluid body rotating with constant angular velocity \(\omega\) and subject to surface tension. The gravity is either absent or has net effect. The mean curvature H of the surface of a fluid drop is given by (*) 2H\(=dv/dr+v/r\), where \(v=du/ds,\quad z=u(s),\quad r=r(s)\) are equations for a surface of revolution in cylindrical coordinates (r,\(\theta\),z) and s is an arclength parameter along the generating curve. The mathematical treatment of the rotating drop is based on the equation (*) and on the theory of elliptic integrals. It is shown that a large family of rotationally symmetric toroidal rotating drops exists and estimates on the possible rates of rotation are derived. The question of stability was not discussed.

Reviewer: A.V.Fedorov

### MSC:

76T99 | Multiphase and multicomponent flows |

34A12 | Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations |