Global well-posedness and scattering for the energy-critical, defocusing Hartree equation for radial data
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چکیده
We consider the defocusing, ˙ H 1-critical Hartree equation for the radial data in all dimensions (n ≥ 5). We show the global well-posedness and scattering results in the energy space. The new ingredient in this paper is that we first take advantage of the term − I |x|≤A|I| 1/2 |u| 2 ∆ 1 |x| dxdt in the localized Morawetz identity to rule out the possibility of energy concentration, instead of the classical Morawetz estimate dependent of the nonlinearity.
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تاریخ انتشار 2008