Rotating solutions to the incompressible Euler-Poisson equation with external particle

We consider a two-dimensional, incompressible fluid body, together with self-induced interactions. The body is perturbed by an external particle with small mass. The whole configuration rotates uniformly around the common center of mass. We construct solutions, which are stationary in a rotating coordinate system, using perturbative methods. In addition, we consider a large class of internal motions of the fluid. The angular velocity is related to the position of the external particle and is chosen to satisfy a non-resonance condition.