Global well-posedness and scattering for the defocusing Hartree equation in R3

We consider the defocusing -subcritical Hartree equation i∂tu+Δu=(|x|−γ*2|u|)u (2<γ<3) in R3. We prove its global well-posedness and scattering property in Hs(R3) 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.