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Global strong solutions of the coupled Klein-Gordon-Schr\"{o}dinger equations

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Tohru Ozawa, Kenta Tomioka

Analysis of PDEs · Submitted 16 Dec 2022

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

The authors' main claim Under natural assumptions on the initial data, we prove the existence and uniqueness of global solutions in $H^2 \oplus H^2 \oplus H^1$.

how it is stated · asserted 1.00 read the record →

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arXiv ID2212.08575 (version 1)
Pith IDXUIHWWVE, Pith's permanent record of this paper and its review
CitationKenta Tomioka, Tohru Ozawa. "Global strong solutions of the coupled Klein-Gordon-Schr\"{o}dinger equations." arXiv:2212.08575 (2022). https://pith.science/paper/XUIHWWVE
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,757 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.36 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.43 · compares with prior results 0.60 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

We study the initial-boundary value problem for the coupled Klein-Gordon-Schr\"{o}dinger equations in a domain in $\mathbb R^N$ with $N \leq 4$. Under natural assumptions on the initial data, we prove the existence and uniqueness of global solutions in $H^2 \oplus H^2 \oplus H^1$. The method of the construction of global strong solutions depends on the proof that solutions of regularized systems by the Yosida approximation form a bounded sequence in $H^2 \oplus H^2 \oplus H^1$ and a convergent sequence in $H^1 \oplus H^1 \oplus L^2$. The method of proof is independent of the Brezis-Gallouet technique and a compactness argument.

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 study the initial-boundary value problem for the coupled Klein-Gordon-Schr\"{o}dinger equations in a domain in $\mathbb R^N$ with $N \leq 4$. background 0.63 0.81 0.03 asserted 0.80
s1 Under natural assumptions on the initial data, we prove the existence and uniqueness of global solutions in $H^2 \oplus H^2 \oplus H^1$. result 0.98 0.96 0.91 asserted 1.00
s2 The method of the construction of global strong solutions depends on the proof that solutions of regularized systems by the Yosida approximation form a bounded sequence in $H^2 \oplus H^2 \oplus H^1$ and a convergent sequence in $H^1 \oplus H^1 \oplus L^2$. method 1.00 0.91 0.06 asserted 1.00
s3 The method of proof is independent of the Brezis-Gallouet technique and a compactness argument. method 0.70 0.81 0.03 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 initial-boundary value problem for the coupled Klein-Gordon-Schr\"{o}dinger equations in a domain in $\mathbb R^N$ with $N \leq 4$. Under natural assumptions on the initial data, we prove the existence and uniqueness of global solutions in $H^2 \oplus H^2 \oplus H^1$. The method of the construction of global strong solutions depends on the proof that solutions of regularized systems by the Yosida approximation form a bounded sequence in $H^2 \oplus H^2 \oplus H^1$ and a convergent sequence in $H^1 \oplus H^1 \oplus L^2$. The method of proof is independent of the Brezis-Gallouet technique and a compactness argument.

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