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 = {}, 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 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 & Lifeng Zhao. (2019). The Cauchy Problem of the Hartree Equation. Journal of Partial Differential Equations. 21 (1). 22-44. doi:
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