Global well-posedness for the defocusing Hartree equation with radial data in R4

By I-method, the interaction Morawetz estimate, long-time Strichartz estimate and local smoothing effect of Schrodinger operator, we show global well-posedness and scattering for the defocusing Hartree equation {iut + Delta u = F(u), (t,x) is an element of R x R-4 u(0) = u(0) (x) is an element of H-s (R-4), where F(u) = (V * vertical bar u vertical bar(2))u, and V (x) = vertical bar x vertical bar(-gamma), 3 < gamma < 4, with radial data in H-s(R-4) for s > s(c) := gamma/2 - 1. It is a sharp global result except the critical case s = s(c), which is a very difficult open problem.