Regular solutions of a problem coupling a compressible fluid and an elastic structure

Boulakia, Muriel; Guerrero, Sergio

doi:10.1016/j.matpur.2010.04.002

Cited by 35 publications

(34 citation statements)

References 18 publications

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“…Subsequent results pertaining to local theories but with lesser requirements imposed on the smoothness of initial data appeared in [KT1,KT2,IKLT1]. Similar results were also obtained for the case of compressible flows [BG1,BG2,KT3].…”

Section: Introductionsupporting

confidence: 65%

Small data global existence for a fluid-structure model

et al. 2017

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We address the system of partial differential equations modeling motion of an elastic body inside an incompressible fluid. The fluid is modeled by the incompressible Navier-Stokes equations while the structure is represented by the damped wave equation with interior damping. The additional boundary stabilization γ, considered in our previous paper, is no longer necessary. We prove the global existence and exponential decay of solutions for small initial data in a suitable Sobolev space.

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Section: Introductionsupporting

confidence: 65%

Small data global existence for a fluid-structure model

et al. 2017

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“…These estimates rely strongly on the previous elliptic results and on the fact that the system is studied without decoupling the fluid and structure. The decoupling allows to take advantage of the specificities of each sub problems [3,19,20,24]. Nevertheless, this method enhances the gap of regularities between each sub-problem, leading to the need of adding some viscosity [19,20] or deriving additionnal hidden regularity [24].…”

Section: Introductionmentioning

confidence: 99%

Existence of local strong solutions to fluid–beam and fluid–rod interaction systems

Grandmont

Hillairet

Lequeurre

2019

Ann. Inst. H. Poincaré Anal. Non Linéaire

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We study an unsteady nonlinear fluid-structure interaction problem. We consider a Newtonian incompressible two-dimensional flow described by the Navier-Stokes equations set in an unknown domain depending on the displacement of a structure, which itself satisfies a linear wave equation or a linear beam equation. The fluid and the structure systems are coupled via interface conditions prescribing the continuity of the velocities at the fluid-structure interface and the action-reaction principle. We prove existence of a unique local-in-time strong solution. In the case of a damped beam this is an alternative proof (and a generalization) of the result that can be found in [19]. In the case of the wave equation or a beam equation with inertia of rotation, this is, to our knowledge the first result of existence of strong solutions for which no viscosity is added. One key point, is to use the fluid dissipation to control, in appropriate function spaces, the structure velocity.

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“…9 by Coutand and Shkoller with initial fluid velocity u 0 belonging to H 5 and initial data for the wave equation (w 0 , w 1 ) belonging to H 3 × H 2 . However, due to the divergence-free condition, the uniqueness for the model required higher regularity data, and it was proved for (u 0 , w 0 , w 1 ) ∈ H 7 × H 5 × H 4 . In Ref.…”

Section: Introductionmentioning

confidence: 99%