In this paper we consider a coupled Wave-Klein–Gordon system in 3 D, and prove global regularity and modified scattering for small and smooth initial data with suitable decay at infinity. This system was derived by W...In this paper we consider a coupled Wave-Klein–Gordon system in 3 D, and prove global regularity and modified scattering for small and smooth initial data with suitable decay at infinity. This system was derived by Wang and LeFloch–Ma as a simplified model for the global nonlinear stability of the Minkowski space-time for self-gravitating massive fields.展开更多
We construct(modified)scattering operators for the Vlasov-Poisson system in three dimensions,mapping small asymptotic dynamics as t→−∞to asymptotic dynamics as t→+∞.The main novelty is the construction of modified...We construct(modified)scattering operators for the Vlasov-Poisson system in three dimensions,mapping small asymptotic dynamics as t→−∞to asymptotic dynamics as t→+∞.The main novelty is the construction of modified wave operators,but we also obtain a new simple proof of modified scattering.Our analysis is guided by the Hamiltonian structure of the Vlasov-Poisson system.Via a pseudo-conformal inversion,we recast the question of asymptotic behavior in terms of local in time dynamics of a new equation with singular coefficients which is approximately integrated using a generating function.展开更多
基金supported in part by NSF(Grant No.DMS-1600028)NSF-FRG(Grant No.DMS-1463753)+1 种基金supported in part by NSF(Grant No.DMS-1362940)by a Sloan Research fellowship
文摘In this paper we consider a coupled Wave-Klein–Gordon system in 3 D, and prove global regularity and modified scattering for small and smooth initial data with suitable decay at infinity. This system was derived by Wang and LeFloch–Ma as a simplified model for the global nonlinear stability of the Minkowski space-time for self-gravitating massive fields.
基金Open Access funding provided by EPFL LausanneThe authors were supported in part by NSF grant DMS-17000282.
文摘We construct(modified)scattering operators for the Vlasov-Poisson system in three dimensions,mapping small asymptotic dynamics as t→−∞to asymptotic dynamics as t→+∞.The main novelty is the construction of modified wave operators,but we also obtain a new simple proof of modified scattering.Our analysis is guided by the Hamiltonian structure of the Vlasov-Poisson system.Via a pseudo-conformal inversion,we recast the question of asymptotic behavior in terms of local in time dynamics of a new equation with singular coefficients which is approximately integrated using a generating function.
