Blow-up for the focusing energy critical nonlinear Schrödinger equation with confining harmonic potential

Xing Cheng; Yanfang Gao

Blow-up for the focusing energy critical nonlinear Schrödinger equation with confining harmonic potential

Xing Cheng; Yanfang Gao

Colloquium Mathematicae (2014)

Volume: 134, Issue: 1, page 143-149
ISSN: 0010-1354

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Abstract

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The focusing nonlinear Schrödinger equation (NLS) with confining harmonic potential

i \partial_{t} u + 1 / 2 Δ u - 1 / 2 | x | ² u = - {| u |}^{4 / (d - 2)} u, x \in ℝ^{d}

, is considered. By modifying a variational technique, we shall give a sufficient condition under which the corresponding solution blows up.

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Xing Cheng, and Yanfang Gao. "Blow-up for the focusing energy critical nonlinear Schrödinger equation with confining harmonic potential." Colloquium Mathematicae 134.1 (2014): 143-149. <http://eudml.org/doc/284377>.

@article{XingCheng2014,
abstract = {The focusing nonlinear Schrödinger equation (NLS) with confining harmonic potential $i∂_t u + 1/2 Δu - 1/2 |x|²u = -|u|^\{4/(d-2)\}u, x ∈ ℝ^\{d\}$, is considered. By modifying a variational technique, we shall give a sufficient condition under which the corresponding solution blows up.},
author = {Xing Cheng, Yanfang Gao},
journal = {Colloquium Mathematicae},
keywords = {nonlinear Schrödinger equation; energy-critical; harmonic potential; blow-up},
language = {eng},
number = {1},
pages = {143-149},
title = {Blow-up for the focusing energy critical nonlinear Schrödinger equation with confining harmonic potential},
url = {http://eudml.org/doc/284377},
volume = {134},
year = {2014},
}

TY - JOUR
AU - Xing Cheng
AU - Yanfang Gao
TI - Blow-up for the focusing energy critical nonlinear Schrödinger equation with confining harmonic potential
JO - Colloquium Mathematicae
PY - 2014
VL - 134
IS - 1
SP - 143
EP - 149
AB - The focusing nonlinear Schrödinger equation (NLS) with confining harmonic potential $i∂_t u + 1/2 Δu - 1/2 |x|²u = -|u|^{4/(d-2)}u, x ∈ ℝ^{d}$, is considered. By modifying a variational technique, we shall give a sufficient condition under which the corresponding solution blows up.
LA - eng
KW - nonlinear Schrödinger equation; energy-critical; harmonic potential; blow-up
UR - http://eudml.org/doc/284377
ER -

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