On a nonlinear fluid-structure interaction problem defined on a domain depending on time

Flori, Fabien; Orenga, Pierre

doi:10.1016/s0362-546x(98)00124-2

Cited by 20 publications

(18 citation statements)

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“…The equations (11,12,13) completed with the structure constitutive equation (5) enable us to associate to a given displacement b another displacement u(b). We denote by S this mapping.…”

Section: Resultsmentioning

confidence: 99%

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Existence for a Three-Dimensional Steady State Fluid-Structure Interaction Problem

Grandmont

2002

Journal of Mathematical Fluid Mechanics

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A steady state fluid-structure interaction problem is considered and its solvability is studied. Both the fluid and the structure are three-dimensional. The equations of the viscous fluid motion are set in an unknown domain depending on the structure displacement. The structure is elastic and its deformation depends on the stress coming from the fluid. We prove that, for small enough applied exterior forces, there exists at least one regular solution of this nonlinear coupled problem. Mathematics Subject Classification (2000). 76D03, 74F10, 35Q30, 35Q35.

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“…The equations (11,12,13) completed with the structure constitutive equation (5) enable us to associate to a given displacement b another displacement u(b). We denote by S this mapping.…”

Section: Resultsmentioning

confidence: 99%

“…For an existence result on a plate interacting with a linear Vol. 4 (2002) Existence for Fluid-Structure Interaction Problem 77 compressible flow, we refer to [11], [12].…”

Section: Introductionmentioning

confidence: 99%

Existence for a Three-Dimensional Steady State Fluid-Structure Interaction Problem

Grandmont

2002

Journal of Mathematical Fluid Mechanics

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“…This survey follows a series of papers [9][10][11][12] dealing with fluid structure interaction problems in which a thin structure (plate or shell) surrounds a domain occupied by a compressible fluid. In these papers, we give existence results in which the proofs are based on approximate solutions constructed by using a fixed point method which connects the fluid problem and the structure equation.…”

Section: Concluding Remarkmentioning

confidence: 99%

“…Our survey follows a series of papers [9][10][11][12], dealing with models defined on a domain depending on time. To solve the problem, the above papers use a method based on a fixed point theorem.…”

Section: Introductionmentioning

confidence: 99%

An existence result for a free boundary shallow water model using a Lagrangian scheme

Flori¹,

Orenga²,

Peybernes³

2008

Ann. Inst. H. Poincaré C Anal. Non Linéaire

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We propose a free boundary shallow water model for which we give an existence theorem. The proof uses an original Lagrangian discrete scheme in order to build a sequence of approximate solutions. The properties of this scheme allow to treat the difficulties linked to the boundary motion. These approximate solutions verify some compactness results which allow us to pass to the limit in the discrete problem. Résumé Nous proposons un modèle de shallow water à frontière libre pour lequel nous donnons un théorème d'existence. La preuve utilise un schéma de discrétisation lagrangien original afin de construire une suite de solutions approchées. Les propriétés de ce schéma permettent de traiter les difficultés liées au mouvement de la frontière. Ces solutions approchées vérifient certaines estimations qui nous permettent de passer à la limite dans le problème discrétisé.

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“…which the structure is a plate occupying a part of the fluid domain boundary. This problem has been already analyzed in a previous study [4] in a two dimensional situation. This first work already pointed out an important difficulty.…”

Section: Introductionmentioning

confidence: 99%

Fluid-structure interaction: analysis of a 3-D compressible model

Flori

Orenga

2000

Ann. Inst. H. Poincaré C Anal. Non Linéaire

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On a nonlinear fluid-structure interaction problem defined on a domain depending on time

Cited by 20 publications

References 0 publications

Existence for a Three-Dimensional Steady State Fluid-Structure Interaction Problem

Existence for a Three-Dimensional Steady State Fluid-Structure Interaction Problem

An existence result for a free boundary shallow water model using a Lagrangian scheme

Fluid-structure interaction: analysis of a 3-D compressible model

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