Flexibility and Rigidity in Steady Fluid Motion

Flexibility and rigidity properties of steady (time-independent) solutions of the Euler, Boussinesq and Magnetohydrostatic equations are investigated. Specifically, certain Liouville-type theorems are established which show that suitable steady solutions with no stagnation points occupying a two-dimensional periodic channel, or axisymmetric solutions in (hollowed out) cylinder, must have certain structural symmetries. It is additionally shown that such solutions can be deformed to occupy domains which are themselves small perturbations of the base domain. As application of the general scheme, Arnol'd stable solutions are shown to be structurally stable.

Automated summary

The flexibility and rigidity properties of steady solutions of the Euler, Boussinesq, and Magnetohydrostatic equations were investigated, revealing certain structural symmetries in suitable steady solutions. It was also shown that these solutions can be deformed to occupy small perturbations of the base domain. Additionally, Arnol'd stable solutions were proven to be structurally stable under this scheme.