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Rough solutions of Einstein vacuum equations in CMCSH gauge

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Qian Wang

Analysis of PDEs · Submitted 30 Dec 2011

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

The authors' main claim In this paper, we consider very rough solutions to Cauchy problem for the Einstein vacuum equations in CMC spacial harmonic gauge, and obtain the local well-posedness result in $H^s, s>2$.

how it is stated · asserted 1.00 read the record →

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arXiv ID1201.0049 (version 1)
Pith IDARFYDU4D, Pith's permanent record of this paper and its review
CitationQian Wang. "Rough solutions of Einstein vacuum equations in CMCSH gauge." arXiv:1201.0049 (2011). https://pith.science/paper/ARFYDU4D
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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, 2,409 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.11 · states limitation 0.28 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.88 · compares with prior results 0.66 · mentions code or data availability 0.01.

The abstract, sentence by sentence

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

In this paper, we consider very rough solutions to Cauchy problem for the Einstein vacuum equations in CMC spacial harmonic gauge, and obtain the local well-posedness result in $H^s, s>2$. The novelty of our approach lies in that, without resorting to the standard paradifferential regularization over the rough, Einstein metric $\bg$, we manage to implement the commuting vector field approach to prove Strichartz estimate for geometric wave equation $\Box_\bg \phi=0$ directly.

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 In this paper, we consider very rough solutions to Cauchy problem for the Einstein vacuum equations in CMC spacial harmonic gauge, and obtain the local well-posedness result in $H^s, s>2$. result 0.79 0.95 0.91 asserted 1.00
s1 The novelty of our approach lies in that, without resorting to the standard paradifferential regularization over the rough, Einstein metric $\bg$, we manage to implement the commuting vector field approach to prove Strichartz estimate for geometric wave equation $\Box_\bg \phi=0$ directly. contribution 0.94 0.95 0.07 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.99 · evidence from proof or derivation 1.00.

What was examined, and what was not

sources read
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not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
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  • 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

In this paper, we consider very rough solutions to Cauchy problem for the Einstein vacuum equations in CMC spacial harmonic gauge, and obtain the local well-posedness result in $H^s, s>2$. The novelty of our approach lies in that, without resorting to the standard paradifferential regularization over the rough, Einstein metric $\bg$, we manage to implement the commuting vector field approach to prove Strichartz estimate for geometric wave equation $\Box_\bg \phi=0$ directly.

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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
  • It is conceivable that the result generalises to more general classes of initial data for which local existence and uniqueness of solutions holds, such as e.g. those considered in [ref] , but this remains to be seen.

    On maximal globally hyperbolic vacuum space-times · Introduction · 0.80

What it cites · 5 sentences without a confident label

Uses the method or tool of 1 paper

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