2018
DOI: 10.3934/dcdsb.2018151
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Semigroup well-posedness of a linearized, compressible fluid with an elastic boundary

Abstract: We address semigroup well-posedness of the fluid-structure interaction of a linearized compressible, viscous fluid and an elastic plate (in the absence of rotational inertia). Unlike existing work in the literature, we linearize the compressible Navier-Stokes equations about an arbitrary state (assuming the fluid is barotropic), and so the fluid PDE component of the interaction will generally include a nontrivial ambient flow profile U. The appearance of this term introduces new challenges at the level of the … Show more

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Cited by 17 publications
(82 citation statements)
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“…With this assumption, the flow coupling is inherently nonlinear, introducing additional complexity into the analysis [26]. We view the analyses in [6] and here as first steps, noting that the linear flow problem here is already of great technical complexity and mathematical challenge. We note the more recent references [9,28], each of which focuses on the issue of weak solvability for certain nonlinear, compressible, viscous fluid-structure interactions.…”
Section: )mentioning
confidence: 99%
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“…With this assumption, the flow coupling is inherently nonlinear, introducing additional complexity into the analysis [26]. We view the analyses in [6] and here as first steps, noting that the linear flow problem here is already of great technical complexity and mathematical challenge. We note the more recent references [9,28], each of which focuses on the issue of weak solvability for certain nonlinear, compressible, viscous fluid-structure interactions.…”
Section: )mentioning
confidence: 99%
“…While the linearized interior terms are by now tractable [6], we must supply the fluid equation with the correct boundary conditions on ∂O that will necessarily involve the plate's deflections w on Ω ⊂ ∂O. The full system (with structural equations) will be discussed in detail in the following section; here, we impose the so called impermeability condition on Ω, namely, that no fluid passes through the elastic portion of the boundary during deflection [8,24].…”
Section: )mentioning
confidence: 99%
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