Modified Wave operators for the Hartree equation with repulsive Coulomb potential
arXiv:2411.02737
Abstract
We study the final state problem for the Hartree equation with repulsive Coulomb potential: \[i\partial_t u+\frac{1}{2}Δu-\frac{1}{|x|}u=((-Δ)^{-1}|u|)^2u\] We show the work in \cite{KaMi} can be extended to the Hartree nonlinearity: Given a prescribed asymptotic profile, we construct a unique global solution scattering to the profile. In particular, the existence of the modified wave operators is obtained for sufficiently localized small scattering data.
10 pages