About the stability of Sobolev's system in the case of viscous fluid (Q1273680)

The authors show an important effect of viscosity on the stability of Sobolev's systems (the rotational motion of a top around a fixed point with a cavity filled up with a viscous fluid): for any angular velocity \(\omega\) in Sobolev's system, different from a certain value \(\omega^*\), there is a value of the viscosity \(v(\omega)\) such that, for every \(v>v(\omega)\), the system is unstable. One supposes that the rigid body (and so the inner cavity) is symmetric with respect to the vertical axis and the inner cavity has an order \(m>2\) of symmetry under rotation around this vertical axis.