TY - JOUR
T1 - Local Well-Posedness for the Einstein--Vlasov System
AU - Fajman, David
N1 - Publisher Copyright:
© 2016 Society for Industrial and Applied Mathematics.
PY - 2016
Y1 - 2016
N2 - 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 Poincaré, 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. Ringström, Oxford Math. Monogr., 2013], where the local stability problem for the Einstein-Vlasov system is solved in generalized harmonic gauge.
AB - 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 Poincaré, 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. Ringström, Oxford Math. Monogr., 2013], where the local stability problem for the Einstein-Vlasov system is solved in generalized harmonic gauge.
KW - Einstein equations
KW - Einstein-Vlasov system
KW - local well-posedness
KW - CMC foliation
KW - elliptic-hyperbolic systems
KW - EXISTENCE
KW - EQUATIONS
KW - SYMMETRY
KW - Elliptic-hyperbolic systems
KW - Local well-posedness
UR - http://www.scopus.com/inward/record.url?scp=84994140279&partnerID=8YFLogxK
U2 - 10.1137/15M1030236
DO - 10.1137/15M1030236
M3 - Article
SN - 0036-1410
VL - 48
SP - 3270
EP - 3321
JO - SIAM Journal on Mathematical Analysis
JF - SIAM Journal on Mathematical Analysis
IS - 5
ER -