TY - JOUR
T1 - The Cauchy Problem of the Hartree Equation
AU - Changxing Miao, Guixiang Xu  & Lifeng Zhao
JO - Journal of Partial Differential Equations
VL - 1
SP - 22
EP - 44
PY - 2008
DA - 2008/02
SN - 21
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jpde/5267.html
KW - Hartree equation
KW - well-posedness
KW - illposedness
KW - Galilean invariance
KW - dispersion analysis
KW - scattering
KW - asymptotically free solutions
AB -  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.