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

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

2008-06-09

arxiv.org/abs/0806.1373v3

Mathematics

Analysis of PDEs

Some minor correction on Error estimate made

Scientific paper

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.

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