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arXiv · 2012.14355

Global well-posedness for the cubic nonlinear Schr{\"o}dinger equation with initial lying in $L^{p}$-based Sobolev spaces

Benjamin Dodson·Avraham Soffer·Thomas Spencer
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Abstract

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.

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Benjamin Dodson, Avraham Soffer, Thomas Spencer. 2020-12-28. Global well-posedness for the cubic nonlinear Schr{\"o}dinger equation with initial lying in $L^{p}$-based Sobolev spaces. https://doi.org/10.1063/5.0042321

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