Flexibility and Rigidity in Steady Fluid Motion

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