arXiv Analytics

Sign in

arXiv:0806.1373 [math.AP]AbstractReferencesReviewsResources

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

Myeongju Chae, Soonsik Kwon

Published 2008-06-09, updated 2009-08-06Version 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.

Comments: Some minor correction on Error estimate made
Categories: math.AP
Subjects: 35Q55
Related articles: Most relevant | Search more
arXiv:0704.0665 [math.AP] (Published 2007-04-05, updated 2007-04-15)
Global well-posedness and scattering for the energy-critical, defocusing Hartree equation for radial data
arXiv:0707.3254 [math.AP] (Published 2007-07-22, updated 2009-06-06)
Global well-posedness and scattering for the energy-critical, defocusing Hartree equation in $\mathbb{R}^{1+n}$
arXiv:1807.05841 [math.AP] (Published 2018-07-07)
Global well-posedness for the defocusing Hartree equation with radial data in $\mathbb R^4$

Links

Toolbox