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arXiv · 2608.17100

Almost sure pointwise convergence for the 2D periodic quintic NLS

Daniel Eceizabarrena·Pablo Merino
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Abstract

We prove probabilistic pointwise convergence to the initial datum for the 2D periodic quintic NLS for data in $H^s(\mathbb T^2)$ with $s > 0$. This is an improvement with respect to the deterministic setting, in which convergence is known to fail if $s < 1/3$. The proof is based on a nonlinear maximal characterization for convergence, Bourgain's linear-nonlinear decomposition and the corresponding nonlinear smoothing for which we employ random tensor estimates.

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Daniel Eceizabarrena, Pablo Merino. 2026-08-17. Almost sure pointwise convergence for the 2D periodic quintic NLS. https://arxiv.org/abs/2608.17100

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