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arXiv · 2312.16527

Improved global well-posedness for mass-critical nonlinear Schr\"odinger equations on tori

Robert Schippa
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Abstract

We show new global well-posedness results for mass-critical nonlinear Schr\"odinger equations on tori in one and two dimensions. For the quintic nonlinear Schr\"odinger equation on the circle we show global well-posedness for initial data in $H^s(\mathbb{T})$ for $s>\frac{1}{3}$ and $\| u_0 \|_{L^2(\mathbb{T})} \ll 1$. In two dimensions we show global well-posedness on possibly irrational tori for $s>\frac{3}{5}$. In the focusing case we need a smallness condition for the mass, whereas in the defocusing case large mass is covered.

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Robert Schippa. 2023-12-27. Improved global well-posedness for mass-critical nonlinear Schr\"odinger equations on tori. https://arxiv.org/abs/2312.16527

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