Global well-posedness and scattering for the defocusing Hartree equation in [formula omitted

Abstract

We consider the defocusing H 1 2 -subcritical Hartree equation i ∂ t u + Δ u = ( | x | − γ * | u | 2 ) u ( 2 < γ < 3 ) in R 3 . We prove its global well-posedness and scattering property in H s ( R 3 ) for s > ( 7 − γ ) ( γ − 2 ) / ( γ + 2 ) when γ ⩾ 5 / 2 ; s > 3 ( γ − 2 ) / 2 ( γ − 1 ) when γ < 5 / 2 . This improves the previous work of Miao, Xu and Zhao (2009) [18]. A new ingredient used here is that we apply some bilinear Strichartz estimates.