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arXiv · 1609.04712

On existence of global solutions of the one-dimensional cubic NLS for initial data in the modulation space $M_{p,q}(\mathbb R)$

Leonid Chaichenets·Dirk Hundertmark·Peer Kunstmann·Nikolaos Pattakos
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Abstract

We prove global existence for the one-dimensional cubic non-linear Schr\"odinger equation in modulation spaces $M_{p,p'}$ for $p$ sufficiently close to $2$. In contrast to known results, our result requires no smallness condition on initial data. The proof adapts a splitting method inspired by work of Vargas-Vega and Hyakuna-Tsutsumi to the modulation space setting and exploits polynomial growth of the free Schr\"odinger group on modulation spaces.

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Leonid Chaichenets, Dirk Hundertmark, Peer Kunstmann, Nikolaos Pattakos. 2016-09-15. On existence of global solutions of the one-dimensional cubic NLS for initial data in the modulation space $M_{p,q}(\mathbb R)$. https://doi.org/10.1016/j.jde.2017.04.020

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