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# Modified Scattering for the Boson Star Equation

## Author(s): Pusateri, Fabio Giuseppe

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 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 of such solutions at infinity 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. Publication Date: Dec-2014 Electronic Publication Date: 17-Jul-2014 Citation: Pusateri, Fabio. (2014). Modified Scattering for the Boson Star Equation. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 332 (1203 - 1234. doi:10.1007/s00220-014-2094-x DOI: doi:10.1007/s00220-014-2094-x ISSN: 0010-3616 EISSN: 1432-0916 Pages: 1203 - 1234 Type of Material: Journal Article Journal/Proceeding Title: COMMUNICATIONS IN MATHEMATICAL PHYSICS Version: Author's manuscript

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