### 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 $\bbr^n$, $n\ge 3$

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 Author Chae, Myeongju ♦ Kwon, Soonsik Source arXiv.org Content type Text File Format PDF Date of Submission 2008-06-09 Language English
 Subject Domain (in DDC) Natural sciences & mathematics ♦ Mathematics Subject Keyword Mathematics - Analysis of PDEs ♦ 35Q55 ♦ math 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. Educational Use Research Learning Resource Type Article