Modified scattering for the Boson Star Equation

Understand

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.