## Continuous Dependence for Nonlinear Schr\"odinger Equation in {\large$H^s$}

J. Math. Sci. Univ. Tokyo
Vol. 19 (2012), No. 1, Page 57--68.

Continuous Dependence for Nonlinear Schr\"odinger Equation in {\large$H^s$}
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 $10$. The proof is based on the estimates in the fractional order Besov spaces both for time and space variables.