Pattern selection with \(\mathrm{O}(3)\) symmetry (Q1068218)

In the paper (up to conjugacy) all isotropy subgroups (little groups) for irreducible representations of \(\mathrm{SO}(3)\) and \(\mathrm{O}(3)\) corresponding to the possible planforms for the spherical Bénard problem are determined. A useful criterion of stability of the obtained solutions is given. Physical applications to the study of steady-state solutions of \(\mathrm{O}(3)\)-symmetrical problems such as the buckling of a spherical shell of finite thickness or the thermal conduction and convection of fluid confined between two concentric spherical shells are discussed.