Existence of rotating magnetic stars

Highlights: • Rotating magnetic star modeled by the Euler–Poisson and MHD equations. • First existence proof with both rotation and magnetic field. • The star has an oblate shape for small rotation and magnetic field. -- Abstract: We consider a star as a compressible fluid subject to gravitational and magnetic forces. This leads to an Euler–Poisson system coupled to a magnetic field, which may be regarded as an MHD model together with gravity. The star executes steadily rotating motion about a fixed axis. We prove, for the first time, the existence of such stars provided that the rotation speed and the magnetic field are sufficiently small.