We consider the scattering problem for the Hartree equation with potential|x|<sup>-1</sup>in a space of dimension n≥2.We prove the existence of H<sup>m</sup>-modified wave operator for Hartree...We consider the scattering problem for the Hartree equation with potential|x|<sup>-1</sup>in a space of dimension n≥2.We prove the existence of H<sup>m</sup>-modified wave operator for Hartree equation on a dense set of a neighborhood of zero in H<sup>m</sup>（R<sup>n</sup>）,meanwhile,we obtain also the global existence for the Cauchy problem of Hartree equation in a space of dimension n≥2.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This project is supported by the National Natural Science Foundation of China,19601005
文摘We consider the scattering problem for the Hartree equation with potential|x|<sup>-1</sup>in a space of dimension n≥2.We prove the existence of H<sup>m</sup>-modified wave operator for Hartree equation on a dense set of a neighborhood of zero in H<sup>m</sup>（R<sup>n</sup>）,meanwhile,we obtain also the global existence for the Cauchy problem of Hartree equation in a space of dimension n≥2.
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.
