Global well-posedness for the cubic nonlinear Schr{\"o}dinger equation with initial lying in $L^{p}$-based Sobolev spaces.
2020
In this paper we continue our study [DSS20] of the nonlinear Schr\"odinger equation (NLS) with bounded initial data which do not vanish at infinity. Local well-posedness on $\mathbb{R}$ was proved for real analytic data. Here we prove global well-posedness for the 1D NLS with initial data lying in $L^{p}$ for any $2 < p < \infty$, provided the initial data is sufficiently smooth. We do not use the complete integrability of the cubic nonlinear Schr{\"o}dinger equation.
Keywords:
- Correction
- Source
- Cite
- Save
- Machine Reading By IdeaReader
5
References
0
Citations
NaN
KQI