TY - JOUR

T1 - Modified Scattering for the Boson Star Equation

AU - Pusateri, Fabio

N1 - Funding Information:
The author was supported in part by a Simons Postdoctoral Fellowship and NSF Grant DMS-1265875.
Publisher Copyright:
© 2014, Springer-Verlag Berlin Heidelberg.

PY - 2014/12

Y1 - 2014/12

N2 - 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.

AB - 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.

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U2 - 10.1007/s00220-014-2094-x

DO - 10.1007/s00220-014-2094-x

M3 - Article

AN - SCOPUS:84939891924

SN - 0010-3616

VL - 332

SP - 1203

EP - 1234

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

IS - 3

ER -