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Global well-posedness of the energy-critical stochastic nonlinear Schr\"odinger equation on the three-dimensional torus

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Guopeng Li, Mamoru Okamoto, Liying Tao

Analysis of PDEs · Submitted 21 Jul 2024

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We adapt the atomic spaces framework in the context of the energy-critical nonlinear Schr\"odinger equation, and employ probabilistic perturbation arguments in the context of stochastic PDEs, establishing the global well-posedness of the defocusing energy-critical quintic SNLS in the energy space.

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arXiv ID2407.15108 (version 2)
Pith ID37R34RRT, Pith's permanent record of this paper and its review
CitationGuopeng Li, Liying Tao, Mamoru Okamoto. "Global well-posedness of the energy-critical stochastic nonlinear Schr\"odinger equation on the three-dimensional torus." arXiv:2407.15108 (2024). https://pith.science/paper/37R34RRT
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,039 input tokens.

What the abstract itself states, as probabilities: claims first 0.97 · states limitation 0.09 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.06 · compares with prior results 0.52 · mentions code or data availability 0.01.

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arXiv listing abstract v2. Results and the main claim are underlined; .

We study the Cauchy problem of the defocusing energy-critical stochastic nonlinear Schr\"odinger equation (SNLS) on the three dimensional torus, forced by an additive noise. We adapt the atomic spaces framework in the context of the energy-critical nonlinear Schr\"odinger equation, and employ probabilistic perturbation arguments in the context of stochastic PDEs, establishing the global well-posedness of the defocusing energy-critical quintic SNLS in the energy space. It is the first global well-posedness result for the periodic SNLS in a critical space.

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What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 We study the Cauchy problem of the defocusing energy-critical stochastic nonlinear Schr\"odinger equation (SNLS) on the three dimensional torus, forced by an additive noise. background 0.55 0.83 0.04 asserted 0.82
s1 We adapt the atomic spaces framework in the context of the energy-critical nonlinear Schr\"odinger equation, and employ probabilistic perturbation arguments in the context of stochastic PDEs, establishing the global well-posedness of the defocusing energy-critical quintic SNLS in the energy space. contribution 0.56 0.96 0.87 asserted 1.00
s2 It is the first global well-posedness result for the periodic SNLS in a critical space. contribution 0.43 0.88 0.46 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

We study the Cauchy problem of the defocusing energy-critical stochastic nonlinear Schr\"odinger equation (SNLS) on the three dimensional torus, forced by an additive noise. We adapt the atomic spaces framework in the context of the energy-critical nonlinear Schr\"odinger equation, and employ probabilistic perturbation arguments in the context of stochastic PDEs, establishing the global well-posedness of the defocusing energy-critical quintic SNLS in the energy space. It is the first global well-posedness result for the periodic SNLS in a critical space.

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