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Sharp weights in the Cauchy problem for nonlinear Schrodinger equations with potential

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Rémi Carles (I3M)

Analysis of PDEs · Submitted 19 Sep 2014

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

The authors' main claim For energy-subcritical nonlinearities and at most quadratic potentials, we investigate the necessary decay in space in order for the Cauchy problem to be locally (and globally) well-posed.

how it is stated · asserted 0.96 read the record →

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arXiv ID1409.5759 (version 3)
Pith IDYI3P22IS, Pith's permanent record of this paper and its review
CitationR\'emi Carles (I3M). "Sharp weights in the Cauchy problem for nonlinear Schrodinger equations with potential." arXiv:1409.5759 (2014). https://pith.science/paper/YI3P22IS
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The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,917 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.51 · human participants 0.01 · controlled comparison 0.03 · randomized assignment 0.01 · states quantitative result 0.14 · compares with prior results 0.15 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v3. Results and the main claim are underlined; .

We review different properties related to the Cauchy problem for the (nonlinear) Schrodinger equation with a smooth potential. For energy-subcritical nonlinearities and at most quadratic potentials, we investigate the necessary decay in space in order for the Cauchy problem to be locally (and globally) well-posed. The characterization of the minimal decay is different in the case of super-quadratic potentials.

background contribution method result interpretation main claim

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 review different properties related to the Cauchy problem for the (nonlinear) Schrodinger equation with a smooth potential. background 0.63 0.45 0.05 asserted 0.83
s1 For energy-subcritical nonlinearities and at most quadratic potentials, we investigate the necessary decay in space in order for the Cauchy problem to be locally (and globally) well-posed. contribution 0.98 0.90 0.40 asserted 0.96
s2 The characterization of the minimal decay is different in the case of super-quadratic potentials. result 0.96 0.52 0.22 asserted 1.00

What kind of paper the classifier reports this is: review 0.69 · evidence from proof or derivation 0.57.

What was examined, and what was not

sources read
  • arXiv listing abstract v3
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
levels run
  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

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 review different properties related to the Cauchy problem for the (nonlinear) Schrodinger equation with a smooth potential. For energy-subcritical nonlinearities and at most quadratic potentials, we investigate the necessary decay in space in order for the Cauchy problem to be locally (and globally) well-posed. The characterization of the minimal decay is different in the case of super-quadratic potentials.

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2 arXiv papers cite this in 2 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 1 sentence without a confident label

Cites it as background 1 paper
  • Also a huge literature has been developed around the corresponding perturbed nonlinear equations in $1-D$, to quote the most recent results we mention Carles [ref] , Cuccagna-Georgiev-Visciglia [ref] , Germain-Hani-Walsh [ref] , and all the references therein.

    Scattering for NLS with a delta potential · Introduction · 1.00

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