Future global nonlinear stability of surface symmetric solutions of the Einstein–Vlasov system with a cosmological constant

Abstract

We show future global nonlinear stability of surface symmetric solutions of the Einstein–Vlasov system with a positive cosmological constant. Estimates of higher derivatives of the metric and the matter terms are obtained using an inductive argument. In a recent research monograph Ringström shows future nonlinear stability of (not necessarily symmetric) solutions of the Einstein–Vlasov system with a nonlinear scalar field if certain local estimates on the geometry and the matter terms are fulfilled. We show that these assumptions are satisfied at late times for the case under consideration here which together with Cauchy stability leads to our main conclusion.