Modified scattering for the Boson Star Equation
Abstract
We consider the question of scattering for the boson star equation in three space dimensions. This is a semi-relativistic Klein-Gordon equation with a cubic nonlinearity of Hartree type. We combine weighted estimates, obtained by exploiting a special null structure present in the equation, and a refined asymptotic analysis performed in Fourier space, to obtain global solutions evolving from small and localized Cauchy data. We describe the behavior at infinity of such solutions by identifying a suitable nonlinear asymptotic correction to scattering. As a byproduct of the weighted energy estimates alone, we also obtain global existence and (linear) scattering for solutions of semi-relativistic Hartree equations with potentials decaying faster than Coulomb.
Cite
@article{arxiv.1308.6600,
title = {Modified scattering for the Boson Star Equation},
author = {Fabio Pusateri},
journal= {arXiv preprint arXiv:1308.6600},
year = {2015}
}