Allen Wu (Brown University)

Rapidly Rotating Stars

A rotating star may be modeled as a fluid under self gravity and with a given total mass and prescribed angular velocity. Mathematically this leads to the Euler-Poisson system. In this talk, we present an existence theorem for such stars that are rapidly rotating, depending continuously on the speed of rotation. No previous results using continuation methods allowed rapid rotation. The key tool for the result is global continuation theory via topological degree, combined with a delicate limiting process. The solutions form a connected set K in an appropriate function space. As the speed of rotation increases, we prove that either the supports of the stars in K become unbounded or the density somewhere within the stars becomes unbounded. We permit any equation of state of the form p = ρ^γ ; 6/5 ≤ γ ≤ 2, so long as γ≠ 4/3. This result is joint work with Walter Strauss.