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

TL;DR

This paper constructs stationary rotating solutions for a 2D incompressible fluid with self-interactions and an external particle, using perturbative methods to analyze the effects of external perturbations on internal fluid motions.

Contribution

It introduces a novel perturbative approach to find rotating solutions of the Euler-Poisson system with external particles, expanding understanding of fluid dynamics under external influences.

Findings

Existence of stationary rotating solutions under external perturbations

Relation between angular velocity and external particle position

Applicability to a broad class of internal fluid motions

Abstract

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.