Global well-posedness for the 1D cubic nonlinear Schr\"odinger equation in $L^p,\,p>2$

Ryosuke Hyakuna

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arXiv · 2506.08554

Global well-posedness for the 1D cubic nonlinear Schr\"odinger equation in $L^p,\,p>2$

Ryosuke Hyakuna

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Abstract

In this paper, we show that the one dimensional cubic nonlinear Schr\"odinger equation is globally well posed in $L^p$ for $2\le p <13/6$. In particular, we prove that the global solution enjoys the persistence property for a twisted variable at any time, which implies the result is a natural exetension of the classical global well-posedness in $L^2$ to $L^p$. The proof exploits the data-decomposition argument originally developed by Vargas-Vega in the functional framework introduced by Zhou.

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Ryosuke Hyakuna. 2025-06-10. Global well-posedness for the 1D cubic nonlinear Schr\"odinger equation in $L^p,\,p>2$. https://arxiv.org/abs/2506.08554

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