On blow-up for the Hartree equation

Jiqiang Zheng. "On blow-up for the Hartree equation." Colloquium Mathematicae 126.1 (2012): 111-124. <http://eudml.org/doc/283849>.

@article{JiqiangZheng2012,
abstract = {We study the blow-up of solutions to the focusing Hartree equation $iu_\{t\} + Δu + (|x|^\{-γ\}*|u|²)u = 0$. 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.},
author = {Jiqiang Zheng},
journal = {Colloquium Mathematicae},
keywords = {Hartree equation; blow-up; Hardy-Littlewood-Sobolev type inequality},
language = {eng},
number = {1},
pages = {111-124},
title = {On blow-up for the Hartree equation},
url = {http://eudml.org/doc/283849},
volume = {126},
year = {2012},
}

TY - JOUR
AU - Jiqiang Zheng
TI - On blow-up for the Hartree equation
JO - Colloquium Mathematicae
PY - 2012
VL - 126
IS - 1
SP - 111
EP - 124
AB - We study the blow-up of solutions to the focusing Hartree equation $iu_{t} + Δu + (|x|^{-γ}*|u|²)u = 0$. 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.
LA - eng
KW - Hartree equation; blow-up; Hardy-Littlewood-Sobolev type inequality
UR - http://eudml.org/doc/283849
ER -