Existence and uniqueness of strong solutions for the system of interaction between a compressible Navier–Stokes–Fourier fluid and a damped plate equation

Maity, Debayan; Takahashi, Takéo

doi:10.1016/j.nonrwa.2020.103267

Cited by 27 publications

(23 citation statements)

References 26 publications

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“…The mostly investigated case is the fluidbeam/plate systems where the beam/plate equation was imposed with different mechanical mechanism (rigidity, stretching, friction, rotation, etc. ), readers are refer to [8,17,21,22,30,31,34,36] and references therein. Moreover, the fluid-structure interaction problems with nonlinear shells were studied in [12,13,33].…”

Section: ĵEmentioning

confidence: 99%

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On a fluid-structure interaction problem for plaque growth

Abels¹,

Liu²

2021

Preprint

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We study a free-boundary fluid-structure interaction problem with growth, which arises from the plaque formation in blood vessels. The fluid is described by the incompressible Navier-Stokes equation, while the structure is considered as a viscoelastic incompressible neo-Hookean material. Moreover, the growth due to the biochemical process is taken into account. Applying the maximal regularity theory to a linearization of the equations, along with a deformation mapping, we prove the well-posedness of the full nonlinear problem via the contraction mapping principle.

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Section: ĵEmentioning

confidence: 99%

“…Moreover, the fluid-structure interaction problems with nonlinear shells were studied in [12,13,33]. It has to be mentioned that in the recent works [17,34], a maximal regularity framework, which requires lower initial regularity and less compatibility conditions compared to the energy method, was employed. 1.5.…”

Section: ĵEmentioning

confidence: 99%

On a fluid-structure interaction problem for plaque growth

Abels¹,

Liu²

2021

Preprint

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“…Considering strong solutions, one can find related results in e.g. [3,14,16,25,26,30,34] and the references therein. Moreover, the fluid-structure interaction problems with linear/nonlinear shells were studied in e.g.…”

Section: Introductionmentioning

confidence: 99%

“…[9,10,28] for strong solutions respectively. It is worth mentioning that in recent works [14,30], a maximal regularity framework, which requires lower initial regularity and less compatibility conditions compared to the energy method, was employed.…”

Section: Introductionmentioning

confidence: 99%

On a fluid-structure interaction problem for plaque growth: cylindrical domain

Abels¹,

Liu²

2021

Preprint

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This paper concerns a free-boundary fluid-structure interaction problem for plaque growth proposed by Yang et al. [J. Math. Biol., 72(4):973-996, 2016] with additional viscoelastic effects, which was also investigated by the authors [arXiv preprint: 2110[arXiv preprint: .00042, 2021. Compared to it, the problem is posed in a cylindrical domain with ninety-degree contact angles, which brings additional difficulties when we deal with the linearization of the system. By a reflection argument, we obtain the existence and uniqueness of strong solutions to the model problems for the linear systems, which are then shown to be well-posed in a cylindrical (annular) domain via a localization procedure. Finally, we prove that the full nonlinear system admits a unique strong solution locally with the aid of the contraction mapping principle.

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“…Using similar techniques they also analyze the case of the wave equation (α 1 = δ = 0 and α 2 > 0) in [1] showing in particular that the semigroup of the linearized system is analytic. Let us mention also some results for more complex models: [29,28] (linear elastic Koiter shell), [38] (dynamic pressure boundary conditions), [39,40] (3D cylindrical domain with nonlinear elastic cylindrical Koiter shell), [49] and [50] (nonlinear elastic and thermoelastic plate equations), [32], [34] (compressible fluids), etc.…”

Section: Introductionmentioning

confidence: 99%

Controllability of a simplified fluid-structure interaction system

Buffe¹,

Takahashi²

2021

Preprint

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We are interested by the controllability of a fluid-structure interaction system where the fluid is viscous and incompressible and where the structure is elastic and located on a part of the boundary of the fluid's domain. In this article, we simplify this system by considering a linearization and by replacing the wave/plate equation for the structure by a heat equation. We show that the corresponding system coupling the Stokes equations with a heat equation at its boundary is null-controllable. The proof is based on Carleman estimates and interpolation inequalities. One of the Carleman estimates corresponds to the case of Ventcel boundary conditions. This work can be seen as a first step to handle the real system where the structure is modeled by the wave or the plate equation.

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Existence and uniqueness of strong solutions for the system of interaction between a compressible Navier–Stokes–Fourier fluid and a damped plate equation

Cited by 27 publications

References 26 publications

On a fluid-structure interaction problem for plaque growth

On a fluid-structure interaction problem for plaque growth

On a fluid-structure interaction problem for plaque growth: cylindrical domain

Controllability of a simplified fluid-structure interaction system

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