2012/05/22 by J. Ginibre, G. Velo, Ginibre, J. +1
Mathematics · Physics and Astronomy · #35P25 (Primary) 35B40 #35Q40 #81U99 (Secondary) #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.AP #math.MP #msc:35B40 #msc:35P25 #msc:35Q40 #msc:81U99
paper · pdf · doi:10.48550/arxiv.1205.4943
41 pages; 12-33. arXiv admin note: text overlap with arXiv:1103.1538
arxiv created 2012/11/19 · arxiv updated 2012/11/20
We reconsider the theory of scattering for some long range Hartree equations with potential |x|-gamma with 1/2 < gamma < 1. More precisely we study the local Cauchy problem with infinite initial time, which is the main step in the construction of the modified wave operators. We solve that problem in the whole subcritical range without loss of regularity between the asymptotic state and the solution, thereby recovering a result of Nakanishi. Our method starts from a different parametrization of the solutions, already used in our previous papers. This reduces the proofs to energy estimates and avoids delicate phase estimates.