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

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