Abstract
The purpose of this work is to identify a sharp criterion under which energy solutions of L 2 supercritical Hartree equation scatter. From the view of physical point, the criterion is represented in terms of the corresponding Lagrange functional and the virial quantity. This differs from Duyckaers et al. (Math Res Lett 15(6):1233–1250, 2008) where the criterion for the nonlinear Schrödinger equation is expressed by the mass-energy product. We shall prove in the Hartree case that these two descriptions are equivalent modulo scaling. Besides, we shall provide a third equivalent description, which is represented in terms of the linear energy. Moreover, the limit of the finite time blow-up solution at blow-up time shall be investigated.
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Gao, Y., Wang, Z. Scattering versus blow-up for the focusing L 2 supercritical Hartree equation. Z. Angew. Math. Phys. 65, 179–202 (2014). https://doi.org/10.1007/s00033-013-0326-0
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DOI: https://doi.org/10.1007/s00033-013-0326-0