GLOBAL WELL-POSEDNESS FOR THE L-2-CRITICAL HARTREE EQUATION ON R-n, n >= 3

Abstract

We consider the initial value problem for the L-2-critical defocusing Hartree equation in R-n, n >= 3. We show that the problem is globally well posed in H-s(R-n) when 1 > s > 2(n-2)/3n-4. We use the "I-method" following [9] combined with a local in time Morawetz estimate for the smoothed out solution I phi as in [7].