On slowly rotating axisymmetric solutions of the Euler-Poisson equations

Abstract

We construct stationary axisymmetric solutions of the Euler-Poisson equations, which govern the internal structure of polytropic gaseous stars, with small constant angular velocity when the adiabatic exponent $\gamma$ belongs to $(\frac{6}{5},\frac{3}{2}]$. The problem is formulated as a nonlinear integral equation, and is solved by iteration technique. By this method, not only we get the existence, but also we clarify properties of the solutions such as the physical vacuum condition and oblateness of the star surface.

References in corpus (2)

• Existence and Nonlinear Stability of Rotating Star Solutions of the Compressible Euler-Poisson Equations
• An Application of the Nash-Moser Theorem to the Vacuum Boundary Problem of Gaseous Stars

Cited by in corpus (9)

• On Rotating Axisymmetric Solutions of the Euler-Poisson Equations
• Rapidly Rotating White Dwarfs
• On slowly rotating axisymmetric solutions of the Einstein-Euler equations
• Stability of rotating gaseous stars
• Existence and uniqueness of compact rotating configurations in GR in second order perturbation theory
• A Remark on the Matter-Vacuum Matching Problem for Axisymmetric Metrics Governed by the Einstein-Euler Equations
• On the axisymmetric metric generated by a rotating perfect fluid with the vacuum boundary
• Rapidly Rotating Stars
• Existence of Rotating Stars with Variable Entropy