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Variational methods for fluid-structure interaction and porous media

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B. Benesova, M. Kampschulte, S. Schwarzacher

Analysis of PDEs · Submitted 23 Jan 2021

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

The authors' main claim By a variational approach we show existence of weak solutions for a class of such coupled systems.

how it is stated · asserted 1.00 read the record →

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arXiv ID2101.09578 (version 2)
Pith IDSI3KWRLG, Pith's permanent record of this paper and its review
CitationB. Benesova, M. Kampschulte, S. Schwarzacher. "Variational methods for fluid-structure interaction and porous media." arXiv:2101.09578 (2021). https://pith.science/paper/SI3KWRLG
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,971 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.23 · human participants 0.02 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.04 · compares with prior results 0.04 · mentions code or data availability 0.01.

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

In this work we consider a poroelastic flexible material that may deform largely which is situated in an incompressible fluid driven by the Navier-Stokes equations in two or three space dimensions. By a variational approach we show existence of weak solutions for a class of such coupled systems. We consider the unsteady case, this means that the PDE for the poroelastic solid involves the Frechet derivative of a non-convex functional as well as (second order in time) inertia terms.

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 work we consider a poroelastic flexible material that may deform largely which is situated in an incompressible fluid driven by the Navier-Stokes equations in two or three space dimensions. background 0.71 0.27 0.03 hedged possibility 0.62
s1 By a variational approach we show existence of weak solutions for a class of such coupled systems. result 0.73 0.94 0.83 asserted 1.00
s2 We consider the unsteady case, this means that the PDE for the poroelastic solid involves the Frechet derivative of a non-convex functional as well as (second order in time) inertia terms. contribution 0.51 0.74 0.07 asserted 0.99

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

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  • C citations
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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

In this work we consider a poroelastic flexible material that may deform largely which is situated in an incompressible fluid driven by the Navier-Stokes equations in two or three space dimensions. By a variational approach we show existence of weak solutions for a class of such coupled systems. We consider the unsteady case, this means that the PDE for the poroelastic solid involves the Frechet derivative of a non-convex functional as well as (second order in time) inertia terms.

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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

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Uses the method or tool of 1 paper
  • In particular, for the fluid this implies [equation] Next note that a Minty-type argument (compare [ref] ) allows us to deal with the second order term in $DE(η^(h))$ while the convergence of the first order terms results from compact embeddings and the boundedness of the determinant.

    A variational approach to hyperbolic evolutions and fluid-structure interactions · Convergence to the full problem · 0.96

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