Solving the constraint equation for general free data

Speaker: Xuantao Chen，Sorbonne University             

Inviter: 马思远

Title: Solving the constraint equation for general free data

Language: English

Time & Venue: 2026.08.12  16:15-17:15  思源楼S813

Abstract: We revisit the problem of solving the Einstein constraint equations in vacuum by a new method, which allows us to prescribe four scalar quantities, representing the full dynamical degrees of freedom of the constraint system. We show that once appropriate gauge conditions have been chosen and four scalars freely specified (modulo ℓ ≤ 1 modes), we can rewrite the constraint equations as a well-posed system of coupled transport and elliptic equations on two-spheres. Our method can be applied to construct various types of initial data, including data with arbitrarily fast decay, borderline decay, and short-pulse type data. This is joint work with Sergiu Klainerman.