The Cauchy Problem of the Hartree Equation

By Miao, Chang-xing, Xu, Guixiang, Zhao, Lifeng. Journal of Partial Differential Equations, 2008

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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 H s , s ≥ 1 and the small scattering result in H s for 2 < γ < n and s ≥ 2 − 1. In addition, we study the nonexistence of nontrivial asymptotically free solutions of the Hartree equation.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/bb023e6db6c54a18b071b52c9469179161459f29