Department of Mathematics

Astronomy is arguably the oldest scientific discipline. Precise measurements of the motion of celestial bodies date back to the ancient Babylonians, Chinese, and indigenous peoples outside Eurasia. Yet, the basic objects of study in Astronomy, namely, stars, are not known to exist. By this, I mean that the standard model for describing the dynamics of a star, the Einstein-Euler system with a physical vacuum boundary, is not known to admit existence and uniqueness of solutions. As I’ll explain, this is due to a fundamental difficulty in understanding the mathematics of the fluid-vacuum interface which separates the body of the star from vacuum. This interface displays a singular behavior which is not amenable to current analytic-geometric techniques. In this talk, I’ll present recent progress in this problem which establishes, in the affirmative, existence and uniqueness of solutions to the system in some particular cases. The talk is based on joint works with Ifrim-Tataru and Speck.