Existence of a weak solution to a nonlinear fluid-structure interaction problem with heat exchange

Mácha, Václav; Muha, Boris; Nečasová, Šárka; Roy, Arnab; Trifunović, Srđan

doi:10.1080/03605302.2022.2068425

Cited by 11 publications

(7 citation statements)

References 49 publications

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“…Next, we state a variant of the Korn inequality on domains with varying boundaries. It is obtained similarly as Lemma 2.2 by the application of already proven time independent result on Hölder domains [51,Lemma 3.8].…”

Section: Assumptions (A)mentioning

confidence: 60%

“…In the context of non-Lipschitz domains (without the structure) a result of the form (6.25) was first proved in [45,Lemma 8] and later adapted for fluid-structure interaction problems in [13,Lemma 6.4] and [51,Lemma 3.4]. The proof of Lemma 6.3 can be done by imitating the arguments of [13] since the proof does not depend on the structure of the pressure.…”

Section: Summary Of the Proof Of Theorem 32mentioning

confidence: 99%

“…Instead we add penalization terms both to the structural as well as fluid sub-problems which helps later (while passing τ → 0) in recovering the kinematic coupling condition on the interface. The penalization we use is of Brinkman type and is inspired from [34] (compressible fluids in time dependent domains) and [51] (compressible mono-fluid structure interaction problem). The fluid sub-problem can be solved by imitating step by step the arguments from [60] with very minor modifications.…”

Section: 3mentioning

confidence: 99%

“…In yet another recent article [66], the authors investigate the existence of weak solutions of a system coupling compressible Navier-Stokes and a linear thermoelastic plate equations. Recently the authors of [51] consider a FSI problem with a heat-conducting fluid which is in a thermal equilibrium with a linear thermoelastic structure constituting the fluid-boundary. Finally we wish to refer the readers to a couple of very interesting articles [9] and [12] where the authors develop a variational strategy to deal with a fluid-structure interaction model involving a bulk structure.…”

Section: 3mentioning

confidence: 99%

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Existence of weak solution for a compressible multicomponent fluid structure interaction problem

Kalousek¹,

Mitra²,

Nečasová³

2023

Preprint

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In this article, we analyze a system of PDEs governing the interaction between two compressible mutually noninteracting fluids and a shell of Koiter type encompassing a time dependent 3D domain filled by the fluids. The dynamics of the fluids is modelled by a system resembilng compressible Navier-Stokes equations with a physically realistic pressure depending on densities of both the fluids. In fact in the present article the dependence of the fluid pressure on the densities is analogous to the ones considered in [60] (where the authors deal with a bi-fluid system in a time independent smooth domain). The shell constitutes the boundary of the fluid domain and it possesses a non-linear, nonconvex Koiter energy (of a quite general form). We are interested in the existence of a weak solution to the system until the time-dependent boundary approaches a self-intersection or the Koiter energy degenerates. We first prove a global existence result (until a degeneracy occurs) when the adiabatic exponents solve max{γ, β} > 2 and min{γ, β} > 0, further the densities are comparable and the structure involved is non-dissipative. Next with the assumption that the structure is dissipative we extend our global existence result to the critical case max{γ, β} ≥ 2 and min{γ, β} > 0. The result is achieved in several steps involving, extension of the physical domain, penalization of the interface condition, artificial regularization of the shell energy, added structural dissipation and suitable limit passages depending on uniform estimates. In order to deal with the bi-fluid system we generalize the almost compactness argument developed in [60,68] to the case of time dependent domains with uniform Hölder continuous boundaries. Moreover, the proof of such a compactness result depends on the existence of renormalized continuity equation in time dependent domains.

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Section: Assumptions (A)mentioning

confidence: 60%

Section: Summary Of the Proof Of Theorem 32mentioning

confidence: 99%

Section: 3mentioning

confidence: 99%

Section: 3mentioning

confidence: 99%

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Existence of weak solution for a compressible multicomponent fluid structure interaction problem

Kalousek¹,

Mitra²,

Nečasová³

2023

Preprint

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show abstract

“…[3] and references therein for more details. Concerning strong and weak solutions for other kind of fluids, we refer, e.g., to [4][5][6][7]. We focus on well-posedness results for strong solutions of the Korteweg-type model in what follows.…”

Section: Introductionmentioning

confidence: 99%

Local Solvability for a Compressible Fluid Model of Korteweg Type on General Domains

Inna

Saito

2023

Mathematics

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In this paper, we consider a compressible fluid model of the Korteweg type on general domains in the N-dimensional Euclidean space for N≥2. The Korteweg-type model is employed to describe fluid capillarity effects or liquid–vapor two-phase flows with phase transition as a diffuse interface model. In the Korteweg-type model, the stress tensor is given by the sum of the standard viscous stress tensor and the so-called Korteweg stress tensor, including higher order derivatives of the fluid density. The local existence of strong solutions is proved in an Lp-in-time and Lq-in-space setting, p∈(1,∞) and q∈(N,∞), with additional regularity of the initial density on the basis of maximal regularity for the linearized system.

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A Thermal Fluid–Structure Interaction Problem: Modeling, Variational and Numerical Analysis

Ciorogar

Stavre

2023

J. Math. Fluid Mech.

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Existence of a weak solution to a nonlinear fluid-structure interaction problem with heat exchange

Cited by 11 publications

References 49 publications

Existence of weak solution for a compressible multicomponent fluid structure interaction problem

Existence of weak solution for a compressible multicomponent fluid structure interaction problem

Local Solvability for a Compressible Fluid Model of Korteweg Type on General Domains

A Thermal Fluid–Structure Interaction Problem: Modeling, Variational and Numerical Analysis

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