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arxiv: 0801.3925 · v2 · submitted 2008-01-25 · 🧮 math.AP · math-ph· math.MP

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

classification 🧮 math.AP math-phmath.MP
keywords dataequationglobalhartreemass-criticalscatteringwell-posednesscase
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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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