Global well-posedness for the $L^2$ critical Hartree equation on   $\bbr^n$, $n\ge 3$
  We consider the initial value problem for the L^2-critical defocusing Hartree equation in R^n, n \ge 3. We show that the problem is globally well posed in H^s(R^n) when 1>s> \frac{2(n-2)}{3n-4}$. We use the "I-method" combined with a local in time Morawetz estimate for the smoothed out solution. 
Myeongju Chae, Soonsik Kwon