Modified Wave operators for the Hartree equation with repulsive Coulomb potential
Abstract
We study the final state problem for the Hartree equation with repulsive Coulomb potential: \[i∂t u+12 u-1|x|u=((-)-1|u|)2u\] We show the work in 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.
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