Drift diffusion equations with fractional diffusion on compact Lie groups

Abstract In this work we investigate the well-posed for diffusion equations associated to subelliptic pseudo-differential operators on compact Lie groups. The by strongly elliptic is considered as a special case and in particular fractional with respect Laplacian. general studied within Hörmander classes sub-Riemannian structure group (encoded system of vector fields). Applications sub-Laplacians, powers more corresponding quasi-geostrophic model drift D are investigated. Examples $$\text {SU}(2)$$ SU ( 2 ) problems analysed.