  This paper aims to study time periodic solutions for 3D inviscid
quasi-geostrophic model. We show the existence of non trivial rotating patches
by suitable perturbation of stationary solutions given by generic revolution
shapes around the vertical axis. The construction of those special solutions
are done through bifurcation theory. In general, the spectral problem is very
delicate and strongly depends on the shape of the initial stationary solutions.
More specifically, the spectral study can be related to an eigenvalue problem
of a self-adjoint compact operator. We are able to implement the bifurcation
only from the largest eigenvalues of the operator, which are simple. Additional
difficulties generated by the singularities of the poles are solved through the
use of suitable function spaces with Dirichlet boundary condition type and
refined potential theory with anisotropic kernels.

Analysis of PDEs