GLOBAL WELL-POSEDNESS OF QUASILINEAR WAVE EQUATIONS ON ASYMPTOTICALLY DE SITTER SPACES

摘要: We establish the small data solvability of suitable quasilinear wave and Klein-Gordon equations in high regularity spaces on a geometric class spacetimes including asymptotically de Sitter spaces. obtain our results by proving global invertibility linear operators with coecients L 2 -based function using iterative arguments for non- problems. The analysis is accomplished two parts: Firstly, theory developed means calculus pseudodierential non-smooth coecients, similar to one Beals Reed, manifolds boundary. Secondly, asymptotic behavior solutions studied standard b-analysis, introduced this context Vasy; particular, resonances play an important role.