Journal article
On the Cauchy problem of 3-D energy-critical Schrödinger equations with subcritical perturbations
Journal of Differential Equations, Vol.230(2), pp.422-445
2006
DOI: 10.1016/j.jde.2006.08.010
Abstract
We investigate the global well-posedness, scattering and blow up phenomena when the 3-D quintic nonlinear Schrödinger equation, which is energy-critical, is perturbed by a subcritical nonlinearity
λ
1
|
u
|
p
u
. We find when the quintic term is defocussing, then the solution is always global no matter what the sign of
λ
1
is. Scattering will occur either when the perturbation is defocussing and
4
3
<
p
<
4
or when the mass of the solution is small enough and
4
3
⩽
p
<
4
. When the quintic term is focusing, we show the blow up for certain solutions.
Details
- Title: Subtitle
- On the Cauchy problem of 3-D energy-critical Schrödinger equations with subcritical perturbations
- Creators
- Xiaoyi Zhang - Chinese Academy of Sciences
- Resource Type
- Journal article
- Publication Details
- Journal of Differential Equations, Vol.230(2), pp.422-445
- DOI
- 10.1016/j.jde.2006.08.010
- ISSN
- 0022-0396
- eISSN
- 1090-2732
- Publisher
- Elsevier Inc
- Language
- English
- Date published
- 2006
- Academic Unit
- Mathematics
- Record Identifier
- 9984241156302771
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