We study the blow-up of solutions to the focusing Hartree equation . We use the strategy derived from the almost finite speed of propagation ideas devised by Bourgain (1999) and virial analysis to deduce that the solution with negative energy (E(u₀) < 0) blows up in either finite or infinite time. We also show a result similar to one of Holmer and Roudenko (2010) for the Schrödinger equations using techniques from scattering theory.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm126-1-8,
author = {Jiqiang Zheng},
title = {On blow-up for the Hartree equation},
journal = {Colloquium Mathematicae},
volume = {126},
year = {2012},
pages = {111-124},
zbl = {1238.35114},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm126-1-8}
}
Jiqiang Zheng. On blow-up for the Hartree equation. Colloquium Mathematicae, Tome 126 (2012) pp. 111-124. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm126-1-8/