Global well-posedness and scattering for the mass-critical Hartree equation with radial data

Details Global well-posedness and scattering for the mass-critical Hartree equation with radial data Global well-posedness and scattering for the mass-critical Hartree equation with radial data

2008-01-25

arxiv.org/abs/0801.3925v2

J.Math.Pures Appl.91(2009)49-79

Mathematics

Analysis of PDEs

38 pages, 1 figure

Scientific paper

10.1016/j.matpur.2008.09.003

We establish global well-posedness and scattering for solutions to the
mass-critical nonlinear Hartree equation $iu_t+\Delta u=\pm(|x|^{-2}*|u|^2)u$
for large spherically symmetric $L^2_x(\Bbb{R}^d)$ initial data; in the
focusing case we require, of course, that the mass is strictly less than that
of the ground state.

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