2018/04/15 by Yilun Wu, Walter A. Strauss, Wu, Yilun +1
Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Waves and Solitons #Quantum chaos and dynamical systems
paper · pdf · doi:10.48550/arxiv.1804.05413
openalex publication_date 2018/04/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A rotating star may be modeled as a continuous system of particles attracted to each other by gravity and with a given total mass and prescribed angular velocity. Mathematically this leads to the Euler-Poisson system. We prove an existence theorem for such stars that are rapidly rotating, depending continuously on the speed of rotation. This solves a problem that has been open since Lichtenstein's work in 1933. The key tool is global continuation theory, combined with a delicate limiting process. The solutions form a connected set \mathcal K in an appropriate function space. As the speed of rotation increases, we prove that \it either the supports of the stars in \mathcal K become unbounded or the density somewhere within the stars becomes unbounded. We permit any equation of state of the form p=ργ, 6/5