Continuous Dependence for Nonlinear Schr\"odinger Equation in {\large$H^s$}
Vol. 19 (2012), No. 1, Page 57--68.
Uchizono, Harunori; Wada, Takeshi
Continuous Dependence for Nonlinear Schr\"odinger Equation in {\large$H^s$}
[Full Article (PDF)] [MathSciNet Review (HTML)] [MathSciNet Review (PDF)]
Abstract:
This paper is concerned with the well-posedness, especially with the continuity of the solution map of the nonlinear\break Schr\"{o}dinger equation \[ i \partial_t u + \Delta u = f(u), \quad u(x , 0) = \phi(x) \] on $\mathbf{R}^{n+1}$. Here, $f(u)=c_0 |u|^\sigma u$, $c_0 \in \mathbf{C}$ and $\sigma > 0$. If $1
Mathematics Subject Classification (2010): Primary 35Q55.
Received: 2011-11-17
