On the small rigid body limit in 3D incompressible flows

He, Jiao; Iftimie, Dragoş

doi:10.1112/jlms.12443

Cited by 7 publications

(10 citation statements)

References 21 publications

(55 reference statements)

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“…The remaining part of the paper is devoted to the proof of Theorem 1.1. Similarly to the purely incompressible setting studied by He and Iftimie [11] (cf. also Lacave and Takahashi [16]), the main problem is the rather weak estimate (1.18) that does not allow for a precise identification of the limit trajectory of the body.…”

Section: Resultsmentioning

confidence: 96%

“…can be controlled in W −1,2 exactly as in He and Iftimie [11] since χ is independent of x. As for the latter, we have…”

Section: Constructing a Suitable Class Of Test Functionsmentioning

confidence: 86%

“…Remark 5.4. We want to point out that as observed by He and Iftimie [11], assumption (1.18) holds for the fluid-structure interaction problem if the condition (5.21) satisfies. Observe that the condition (5.21) implies inf ̺ S ε → ∞, where ̺ S ε is the density of the rigid body immersed in the fluid.…”

Section: Appendixmentioning

confidence: 89%

“…by a suitable family of admissible test functions (ϕ ε ) ε>0 in (3.2). The test function are obtained following the construction of He and Iftimie [10,11], specifically,…”

Section: Constructing a Suitable Class Of Test Functionsmentioning

confidence: 99%

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On the motion of a nearly incompressible viscous fluid containing a small rigid body

Feireisl¹,

Zarnescu²

2022

Preprint

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We consider the motion of a compressible viscous fluid containing a moving rigid body confined to a planar domain Ω ⊂ R 2 . The main result states that the influence of the body on the fluid is negligible if (i) the diameter of the body is small and (ii) the fluid is nearly incompressible (the low Mach number regime). The specific shape of the body as well as the boundary conditions on the fluid-body interface are irrelevant and collisions with the boundary ∂Ω are allowed. The rigid body motion may be enforced externally or governed solely by its interaction with the fluid.

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Section: Resultsmentioning

confidence: 96%

“…can be controlled in W −1,2 exactly as in He and Iftimie [11] since χ is independent of x. As for the latter, we have…”

Section: Constructing a Suitable Class Of Test Functionsmentioning

confidence: 86%

Section: Appendixmentioning

confidence: 89%

“…by a suitable family of admissible test functions (ϕ ε ) ε>0 in (3.2). The test function are obtained following the construction of He and Iftimie [10,11], specifically,…”

Section: Constructing a Suitable Class Of Test Functionsmentioning

confidence: 99%

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On the motion of a nearly incompressible viscous fluid containing a small rigid body

Feireisl¹,

Zarnescu²

2022

Preprint

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“…Finally, let us mention that the counterparts in two space dimensions of some of our results in Sections 4-7 have been used in Takahashi and Lacave [16] to study the behaviour of solutions of (1.2) when the radius of the rigid ball tends to zero (see also He and Iftimie [10] and references therein). We believe that the approach in [16] can be adapted to the three dimensional case by using our results on the fluid structure-semigroup and its generator, but this deserves further work.…”

Section: 3)mentioning

confidence: 99%

Large time behaviour for the motion of a solid in a viscous incompressible fluid

2022

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In this article, we study the long-time behaviour of a system describing the coupled motion of a rigid body and of a viscous incompressible fluid in which the rigid body is contained. We assume that the system formed by the rigid body and the fluid fills the entire space R 3 . In the case in which the rigid body is a ball, we prove the local existence of mild solutions and, when the initial data are small, the global existence of solutions for this system with a precise description of their large time behavior. Our main result asserts, in particular, that if the initial datum is small enough in suitable norms then the position of the center of the rigid ball converges to some h ∞ ∈ R 3 as time goes to infinity. This result contrasts with those known for the analogues of our system in 2 or 1 space dimensions, where it has been proved that the body quits any bounded set, provided that we wait long enough. To achieve this result, we use a "monolithic" type approach, which means that we consider a linearized problem in which the equations of the solid and of the fluid are still coupled. An essential role is played by the properties of the semigroup, called fluid-structure semigroup, associated to this coupled linearized problem. The generator of this semigroup is called the fluidstructure operator. Our main tools are new L p − L q estimates for the fluid-structure semigroup. Note that these estimates are proved for bodies of arbitrary shape. The main ingredients used to study the fluid-structure semigroup and its generator are resolvent estimates which provide both the analyticity of the fluid-structure semigroup (in the spirit of a classical work of Borchers and Sohr) and L p − L q decay estimates (by adapting a strategy due to Iwashita).

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On the Motion of a Nearly Incompressible Viscous Fluid Containing a Small Rigid Body

2023

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We consider the motion of a compressible viscous fluid containing a moving rigid body confined to a planar domain $$\Omega \subset R^2$$ Ω ⊂ R 2 . The main result states that the influence of the body on the fluid is negligible if (i) the diameter of the body is small and (ii) the fluid is nearly incompressible (the low Mach number regime). The specific shape of the body as well as the boundary conditions on the fluid–body interface are irrelevant and collisions with the boundary $$\partial \Omega $$ ∂ Ω are allowed. The rigid body motion may be enforced externally or governed solely by its interaction with the fluid.

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On the small rigid body limit in 3D incompressible flows

Cited by 7 publications

References 21 publications

On the motion of a nearly incompressible viscous fluid containing a small rigid body

On the motion of a nearly incompressible viscous fluid containing a small rigid body

Large time behaviour for the motion of a solid in a viscous incompressible fluid

On the Motion of a Nearly Incompressible Viscous Fluid Containing a Small Rigid Body

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