Mass concentration for the $L^2$-critical Nonlinear Schrödinger equations of higher orders
2014.03.24 18:29
| 실적년도 | 2010 년 |
|---|---|
| 논문구분 | 국외 |
| 총저자 | 이상혁 채명주 |
| 학술지명 | DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS |
| 권(Vol.) | |
| 호(No.) | |
| 게재년월 | 년 월 |
| Impact Factor | |
| SCI 등재 | SCI |
| 비고 |
We consider the mass concentration phenomenon for the $L^2$-critical
nonlinear Schr"odinger equations of higher orders. We show that any solution
$u$ to $iu_{t} + (-Delta){}^{fracalpha2} u =pm |u|^frac{2alpha}{d}u$, $u(0,cdot)in L^2$ for $al >2$,
which blows up in a finite time, satisfies a mass concentration phenomenon near the blow-up time.
When $al=2$, the phenomenon was firstly studied by Bourgain cite{bo2} for two dimensional case,
and then was extended for higher dimensions by B'egout-Vargas cite{bv}.
In higher order cases we verify that as $al$ increases, the size of region capturing a mass concentration
gets wider due to the stronger dispersive effect.
