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.

References in corpus (2)

• The Boson star equation with initial data of low regularity
• Nonlinear fractional Schrödinger equations in one dimension

Cited by in corpus (7)

• Selected topics in scalar-tensor theories and beyond
• Asymptotics for 1D Klein-Gordon equations with variable coefficient quadratic nonlinearities
• Small data scattering for semi-relativistic equations with Hartree type nonlinearity
• Global analysis of a model for capillary water waves in 2D
• Small data scattering of 2d Hartree type Dirac equations
• Charge conjugation approach to scattering for the Hartree type Dirac equations with chirality
• Boson Stars with Long-range Perturbations