In this note we study Hartree type equations with |∇| α (1 <α ≤ 2) and potential whose Fourier transform behaves like |ξ| - (d- γ1) at the origin and |ξ| - (d- γ2) at infinity. We show non-existence of scattering when 0 <1 γ ≤ 1 and small data scattering in Hs for s > 2-α/2 when 2 <γ1 ≤ d and 0 <γ2 ≤ 2. For this we use Up - Vp space argument and Strichartz estimate.
ASJC Scopus subject areas
- Applied Mathematics