1009.2005 (Wei Dai et al.)

Continuous Dependence of Cauchy Problem For Nonlinear Schrödinger
Equation in $H^{s}$    [PDF]

Wei Dai, Weihua Yang, Daomin Cao

We consider the Cauchy problem for the nonlinear Schr\"{o}dinger equation $i
\partial_{t}u+ \Delta u=\lambda_{0}u+\lambda_{1}|u|^\alpha u$ in
$\mathbb{R}^{N}$, where $\lambda_{0},\lambda_{1}\in\mathbb{C}$, in $H^s$
subcritical and critical case: $0<\alpha\leq\frac{4}{N-2s}$ when
$1the solution depends continuously on the initial value in the standard sense in
$H^{s}(\mathbb{R}^{N})$ if $\alpha$ satisfies certain assumptions.

View original: http://arxiv.org/abs/1009.2005