Local Well-Posedness for the Einstein--Vlasov System

Abstract

We prove a local well-posedness result for the Einstein--Vlasov system in constant mean curvature--spatial harmonic gauge introduced in [L. Andersson and V. Moncrief, Ann. Henri Poincare, 4 (2003), pp. 1--34], where local well-posedness for the vacuum Einstein equations is established. This work is based on the techniques developed therein. In addition, we use the regularity theory and techniques for proving the existence of solutions to the Einstein--Vlasov system, recently established in [H. Ringstrom, Oxford Math. Monogr., 2013], where the local stability problem for the Einstein--Vlasov system is solved in generalized harmonic gauge.