2013/08/29 by Fabio Pusateri
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Astrophysics #Boson #Cauchy distribution #Fourier transform #Hartree #Klein–Gordon equation #Mathematical analysis #Mathematical physics #Mathematics #Nonlinear system #Numerical methods in inverse problems #Physics #Quantum mechanics #Scattering #Space (punctuation) #Spectral Theory in Mathematical Physics #Star (game theory) #math-ph #math.AP #math.MP #msc:35P25 #msc:35Q40 #msc:35Q55
paper · pdf · doi:10.1007/s00220-014-2094-x
arxiv created 2013/08/29 · openalex publication_date 2014/07/16 · arxiv updated 2015/06/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.