We consider the Cauchy problem for the focusing Hartree equation in ℝ⁵ with initial data in H¹, and study the divergence property of infinite-variance and nonradial solutions. For the ground state solution of in ℝ⁵, we prove that if u₀ ∈ H¹ satisfies M(u₀)E(u₀) < M(Q)E(Q) and ||∇u₀||₂||u₀||₂ > ||∇Q||₂||Q||₂, then the corresponding solution u(t) either blows up in finite forward time, or exists globally for positive time and there exists a time sequence tₙ → ∞ such that ||∇u(tₙ)||₂ → ∞. A similar result holds for negative time.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm125-2-10,
author = {Daomin Cao and Qing Guo},
title = {Divergent solutions to the 5D Hartree equations},
journal = {Colloquium Mathematicae},
volume = {122},
year = {2011},
pages = {255-287},
zbl = {1238.35108},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm125-2-10}
}
Daomin Cao; Qing Guo. Divergent solutions to the 5D Hartree equations. Colloquium Mathematicae, Tome 122 (2011) pp. 255-287. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm125-2-10/