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Volume 21, Issue 1
The Cauchy Problem of the Hartree Equation

Changxing Miao, Guixiang Xu & Lifeng Zhao

J. Part. Diff. Eq., 21 (2008), pp. 22-44.

Published online: 2008-02

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  • 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.
  • Keywords

Hartree equation well-posedness illposedness Galilean invariance dispersion analysis scattering asymptotically free solutions

  • AMS Subject Headings

35Q40 35Q55 47J35.

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JPDE-21-22, author = {Changxing Miao, Guixiang Xu and Lifeng Zhao}, 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} }
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.
Changxing Miao, Guixiang Xu and Lifeng Zhao. (2008). The Cauchy Problem of the Hartree Equation. Journal of Partial Differential Equations. 21 (1). 22-44. doi:
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