Global well-posedness for the $L^2$ critical Hartree equation on $\bbr^n$, $n\ge 3$

Abstract

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.

Some minor correction on Error estimate made

References in corpus (2)

• Global well-posedness and scattering for the mass-critical Hartree equation with radial data
• Improved interaction Morawetz inequalities for the cubic nonlinear Schrödinger equation on ${\mathbb{R}}^2$