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 -