,THE CAUCHY PROBLEM OF THE HARTREE EQUATION

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In this paper, we systematically study the wellposedness, illposedness of the Hartree equation, and obtain the sharp local wellposedness, the global existence in Hs, s≥1 and the small scattering result in Hs for 2 <γ<n and s≥γ/2- 1. In addition, we study the nonexistence of nontrivial asymptotically free solutions of the Hartree equation.
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