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arXiv · 2407.07234

Global well-posedness and scattering for the defocusing septic one-dimensional NLS via new smoothing and almost Morawetz estimates

Zachary Lee·Xueying Yu
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Abstract

In this paper, we show that the one dimensional septic nonlinear Schr\"odinger equation is globally well-posed and scatters in $H^s (\mathbb{R})$ when $s > 19/54$. We prove new smoothing estimates on the nonlinear Duhamel part of the solution and utilize a linear-nonlinear decomposition to take advantage of the gained regularity. We also prove new $L^{p+3}_{t,x}$ almost Morawetz estimates for the defocusing $p-$NLS adapted to the low-regularity setting, before specializing to the septic case $p=7$.

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Zachary Lee, Xueying Yu. 2024-07-09. Global well-posedness and scattering for the defocusing septic one-dimensional NLS via new smoothing and almost Morawetz estimates. https://arxiv.org/abs/2407.07234

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