@Article{JPDE-21-22, author = {}, title = {The Cauchy Problem of the Hartree Equation}, journal = {Journal of Partial Differential Equations}, year = {2008}, volume = {21}, number = {1}, pages = {22--44}, abstract = { In this paper, we systematically study the wellposedness, illposedness of the Hartree equation, and obtain the sharp local wellposedness, the global existence in H^s, s ≥ 1 and the small scattering result in H^s for 2 < γ < n and s ≥ \frac{γ}{2}-1. In addition, we study the nonexistence of nontrivial asymptotically free solutions of the Hartree equation.}, issn = {2079-732X}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jpde/5267.html} }