Convergence to Equilibrium in Wasserstein distance for damped Euler equations with interaction forces

Jos\'e A. Carrillo; Oliver Tse; Young-Pil Choi

RECORD

Convergence to Equilibrium in Wasserstein distance for damped Euler equations with interaction forces

José A. Carrillo, Young-Pil Choi, Oliver Tse

Analysis of PDEs · Submitted 16 Dec 2017

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

The authors' main claim We develop tools to construct Lyapunov functionals on the space of probability measures in order to investigate the convergence to global equilibrium of a damped Euler system under the influence of external and interaction potential forces with respect to the 2-Wasserstein distance.

how it is stated · asserted 0.98 read the record →

Comment (0) Read on arXiv ↗

Cite ▾

arXiv ID1712.05923 (version 2)

Pith ID6K5LBTEV, Pith's permanent record of this paper and its review

CitationJos\'e A. Carrillo, Oliver Tse, Young-Pil Choi. "Convergence to Equilibrium in Wasserstein distance for damped Euler equations with interaction forces." arXiv:1712.05923 (2017). https://pith.science/paper/6K5LBTEV

Claim paper

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.

Open the compiled record

Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,388 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.54 · human participants 0.01 · controlled comparison 0.03 · randomized assignment 0.01 · states quantitative result 0.05 · compares with prior results 0.07 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

We develop tools to construct Lyapunov functionals on the space of probability measures in order to investigate the convergence to global equilibrium of a damped Euler system under the influence of external and interaction potential forces with respect to the 2-Wasserstein distance. We also discuss the overdamped limit to a nonlocal equation used in the modelling of granular media with respect to the 2-Wasserstein distance, and provide rigorous proofs for particular examples in one spatial dimension.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We develop tools to construct Lyapunov functionals on the space of probability measures in order to investigate the convergence to global equilibrium of a damped Euler system under the influence of external and interaction potential forces with respect to the 2-Wasserstein distance.	contribution 0.93	0.95	0.38	asserted 0.98
s1	We also discuss the overdamped limit to a nonlocal equation used in the modelling of granular media with respect to the 2-Wasserstein distance, and provide rigorous proofs for particular examples in one spatial dimension.	contribution 0.99	0.92	0.13	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.55 · evidence from proof or derivation 1.00.

What was examined, and what was not

sources read

arXiv listing abstract v2

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 develop tools to construct Lyapunov functionals on the space of probability measures in order to investigate the convergence to global equilibrium of a damped Euler system under the influence of external and interaction potential forces with respect to the 2-Wasserstein distance. We also discuss the overdamped limit to a nonlocal equation used in the modelling of granular media with respect to the 2-Wasserstein distance, and provide rigorous proofs for particular examples in one spatial dimension.

Human review

How Pith checks papers → · Full audit of this paper →

How the literature uses it

What this paper does with the arXiv papers it cites

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

What it cites

Cites as background 1 paper

However, much less is known in terms of rates of convergence if uniform convexity of the potentials is not present, see [ref] and the references therein for blow-up time, equilibrium solutions and qualitative covergence results.

Nonlinear Aggregation-Diffusion Equations: Radial Symmetry and Long Time Asymptotics · Introduction · 0.86

Discussion

Know something about this paper? Leave a comment, or highlight any passage above to comment on it.