Finite-time contact in fluid-elastic structure interaction: Navier-slip coupling condition

Krutika Tawri; Nash Ward

arxiv: 2604.06362 · v1 · submitted 2026-04-07 · 🧮 math.AP

Finite-time contact in fluid-elastic structure interaction: Navier-slip coupling condition

Krutika Tawri , Nash Ward This is my paper

Pith reviewed 2026-05-10 18:34 UTC · model grok-4.3

classification 🧮 math.AP

keywords fluid-structure interactionfinite-time contactNavier-slip conditionweak solutionselastic tubeNavier-Stokes equationstube collapseplate equations

0 comments

The pith

Weak solutions to the Navier-slip fluid-elastic tube model reach contact in finite time under sufficient pressure drop.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper examines viscous incompressible flow through a thin elastic tube, modeled by 2D Navier-Stokes equations coupled to 1D plate equations. The coupling uses Navier-slip conditions at the moving interface, which introduce tangential velocity jumps beyond standard geometric nonlinearities. After establishing existence of weak solutions and a hidden spatial regularity result for the structure displacement, the central theorem shows that the upper boundary contacts the lower rigid boundary in finite time whenever the imposed pressure drop is large enough. This provides the first rigorous proof of finite-time contact in a fluid-elastic structure interaction system and resolves the no-collision paradox previously identified in the no-slip setting.

Core claim

The central claim is that weak solutions of the fluid-structure interaction problem exist and that, for a sufficiently large pressure drop across the channel, there exists a finite time at which the compliant upper boundary meets the lower rigid boundary. The proof proceeds by first obtaining weak solutions, then deriving additional spatial regularity on the elastic displacement that allows control of the distance to contact, and finally showing that this distance reaches zero in finite time under the pressure condition. This directly addresses and overcomes the no-collision paradox from the corresponding no-slip analysis.

What carries the argument

The Navier-slip coupling condition at the deformable interface, which permits tangential velocity discontinuities between fluid and structure, together with the derived hidden spatial regularity of the elastic displacement that controls the gap to contact.

If this is right

The model is validated for capturing near-contact dynamics in fluid-elastic tubes.
Finite-time contact becomes provable once the no-slip condition is relaxed to Navier-slip.
Weak solutions can be continued up to the moment of contact rather than stopping earlier.
The pressure-drop threshold supplies a concrete criterion that guarantees collapse occurs while the solution remains valid.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

Navier-slip may be the physically appropriate interface condition for modeling tubes that undergo contact in biological or engineering applications.
The regularity technique used to control the gap could be adapted to prove contact in related FSI problems with other slip or friction conditions.
Numerical schemes for this system should be designed to handle the finite-time singularity at contact rather than assuming solutions remain separated for all time.

Load-bearing premise

The imposed pressure drop stays large enough to force collapse before the weak solution ceases to exist or before unmodeled effects such as contact forces intervene.

What would settle it

An explicit weak solution or numerical computation in which the gap between boundaries approaches zero only as time tends to infinity, even when the pressure drop is held above the stated threshold, would disprove the finite-time contact claim.

Figures

Figures reproduced from arXiv: 2604.06362 by Krutika Tawri, Nash Ward.

**Figure 1.** Figure 1: A snapshot of fluid domain For a continuous function h(x, t) : [0, L]×[0,∞) 7→ T, we introduce the notation for fluid domain, Fh(t) := {(x, y) : 0 < x < L, 0 < y < h(x, t)}. In this work, h which determines the location of the elastic structure sitting atop the fluid domain, is itself an unknown in the problem. The time-dependent (deformable) boundary of the fluid domain Fh(t) is given by Γh(t) := {(x, h(x… view at source ↗

read the original abstract

We consider a fluid-structure interaction problem involving a viscous, incompressible fluid flow, modeled by the 2D Navier-Stokes equations, through a thin deformable elastic tube, displacement of which is not known a priori. The elastodynamics problem is given by 1D plate equations. The fluid and the structure are nonlinearly coupled via the kinematic and dynamic coupling conditions at the fluid-structure interface. The fluid flow is driven by dynamic pressure data imposed at the inlet and outlet of the tube. We impose the Navier-slip boundary condition at the deformable fluid-structure interface and at the bottom rigid boundary of the fluid domain. Hence, beyond the usual geometric nonlinearities arising from nonlinear coupling in FSI with no-slip, the analysis is more challenging due to the possibility of tangential jumps of the fluid and structural velocities at the moving interface. We first discuss the existence of weak solutions and then establish a `hidden' spatial regularity result for the structure displacement. Our main result proves the existence of a finite time for weak solutions at which the compliant upper boundary meets the lower boundary (i.e., the tube collapses), provided that there is a sufficient pressure drop across the channel. This resolves the ''no-collision'' paradox identified by Grandmont and Hillairet in the no-slip setting in [Arch. Ration. Mech. Anal., 220(3): 1283-1333, (2016)], the counterpart to the present work. To the best of our knowledge, this is the first work that rigorously establishes finite-time contact in a fluid-elastic structure interaction system, thereby validating the model to correctly capture near-contact dynamics.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper proves finite-time contact for weak solutions in a Navier-slip FSI tube model, extending the no-slip no-collision result, but the pressure-drop threshold stays qualitative.

read the letter

This paper proves that weak solutions to a 2D Navier-Stokes and 1D plate FSI system with Navier-slip at the interface reach contact in finite time when the driving pressure drop is large enough. That is the central new claim, and it directly counters the no-collision result that Grandmont and Hillairet obtained under no-slip conditions in 2016. The authors first construct weak solutions, then extract hidden spatial regularity on the structure displacement, and finally use that regularity to locate the contact time. The program is a standard extension of existing FSI techniques, adapted to allow tangential velocity jumps at the moving boundary. The slip condition makes the model more realistic for near-contact regimes in tubes, and the proof roadmap looks internally consistent on the basis of the abstract. The main soft spot is the pressure condition itself. The statement only requires a “sufficient” drop without an explicit lower bound expressed in terms of the initial data, the energy estimates, or the a priori bounds that control the maximal existence time. If the argument does not derive a concrete comparison showing that the contact time is strictly smaller than the possible blow-up time, the result remains conditional on an unverified inequality. That detail matters for applicability. The work is aimed at researchers who already work on mathematical analysis of fluid-structure interaction, especially those interested in contact problems or slip boundary conditions. A reader following the Grandmont-Hillairet line will see the precise change that slip introduces. I would send the manuscript to referees. The claim is new, the setting is well-motivated, and the technical steps are of the sort that can be checked in review.

Referee Report

2 major / 1 minor

Summary. The manuscript establishes existence of weak solutions to a 2D incompressible Navier-Stokes fluid coupled to a 1D elastic plate structure via nonlinear kinematic/dynamic conditions and Navier-slip boundary conditions at the moving interface and rigid bottom. It derives a hidden spatial regularity result for the structure displacement and proves that, for a sufficiently large imposed pressure drop, the weak solutions reach a finite time at which the upper boundary contacts the lower boundary (tube collapse). This resolves the no-collision paradox known from the no-slip case.

Significance. If the central claims hold, the work supplies the first rigorous existence proof of finite-time contact in a fluid-elastic structure interaction system. By replacing no-slip with Navier-slip, it circumvents the no-collision obstruction identified in prior literature and thereby validates the model for near-contact regimes. The combination of weak-solution existence, hidden regularity, and explicit contact-time result constitutes a substantive advance for mathematical analysis of FSI problems with possible tangential velocity discontinuities.

major comments (2)

[Main theorem (finite-time contact)] Main result on finite-time contact: the statement that contact occurs 'provided that there is a sufficient pressure drop' does not supply an explicit quantitative lower bound on ΔP in terms of the constants appearing in the energy estimates or the hidden-regularity bounds. Without such a comparison, it remains unclear whether the contact time T* is guaranteed to lie strictly before the maximal existence time T_max of the constructed weak solution.
[Hidden regularity result] Hidden regularity section: the passage from the weak formulation to the additional spatial regularity for the plate displacement relies on testing with specific test functions that exploit the Navier-slip condition; the precise integration-by-parts identities and the control of the tangential jump terms should be verified to ensure they close without additional assumptions on the pressure data.

minor comments (1)

[Abstract] The abstract refers to 'dynamic pressure data' imposed at inlet and outlet; the manuscript should clarify whether these data are time-dependent or constant and how their regularity enters the existence and contact-time arguments.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their thorough review and valuable suggestions. We address the major comments point by point below, indicating where revisions will be made to the manuscript.

read point-by-point responses

Referee: Main result on finite-time contact: the statement that contact occurs 'provided that there is a sufficient pressure drop' does not supply an explicit quantitative lower bound on ΔP in terms of the constants appearing in the energy estimates or the hidden-regularity bounds. Without such a comparison, it remains unclear whether the contact time T* is guaranteed to lie strictly before the maximal existence time T_max of the constructed weak solution.

Authors: We appreciate this observation. In our proof, we first derive a priori bounds independent of the contact time, then construct T* explicitly as a function of the initial energy, the hidden regularity constants, and ΔP. We then choose ΔP large enough so that T* is smaller than the time at which the energy bounds would blow up or the maximal time. While the lower bound on ΔP is not given as a closed-form expression with all constants expanded, its existence and dependence are clear from the estimates. We will add a remark in the revised manuscript explicitly stating the dependence of the threshold ΔP on the constants from the energy and regularity estimates to clarify that T* < T_max. revision: partial
Referee: Hidden regularity section: the passage from the weak formulation to the additional spatial regularity for the plate displacement relies on testing with specific test functions that exploit the Navier-slip condition; the precise integration-by-parts identities and the control of the tangential jump terms should be verified to ensure they close without additional assumptions on the pressure data.

Authors: We thank the referee for this suggestion. The hidden regularity is obtained by choosing test functions in the weak form that correspond to the structure equation tested against the displacement, using the Navier-slip to handle the interface terms. The integration by parts is justified by the available regularity (fluid velocity in L^2(0,T; H^1), pressure in L^2, structure in appropriate spaces), and the tangential jump is controlled by the slip length parameter without requiring extra assumptions on the pressure beyond the given data. We will expand the proof in the hidden regularity section with more detailed steps for the integration-by-parts and term estimates to make this verification explicit. revision: yes

Circularity Check

0 steps flagged

No circularity: standard PDE existence proof with external citation

full rationale

The derivation establishes weak solution existence for the Navier-Stokes/plate FSI system with Navier-slip conditions, followed by a hidden regularity result and then finite-time contact under a sufficient pressure drop hypothesis. This chain relies on standard energy estimates, compactness arguments, and an external reference to the no-collision result of Grandmont-Hillairet (different authors). No step reduces by construction to its own inputs: there are no fitted parameters renamed as predictions, no self-definitional quantities, no load-bearing self-citations, and no ansatz smuggled via prior work by the same authors. The 'sufficient pressure drop' is an explicit hypothesis in the main theorem rather than a derived quantity that loops back to the conclusion.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on the prior existence of weak solutions to the coupled system and an intermediate hidden regularity result for the structure; both are treated as established before the main contact theorem. No free parameters or new physical entities are introduced.

axioms (2)

domain assumption Existence of weak solutions to the 2D Navier-Stokes / 1D plate FSI system with Navier-slip coupling
Stated explicitly as the first step before proving the hidden regularity and contact result.
domain assumption Hidden spatial regularity of the structure displacement
Established as an intermediate result required to reach the finite-time contact conclusion.

pith-pipeline@v0.9.0 · 5592 in / 1471 out tokens · 42781 ms · 2026-05-10T18:34:30.733937+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

Our main result proves the existence of a finite time for weak solutions at which the compliant upper boundary meets the lower boundary ... provided that there is a sufficient pressure drop across the channel.

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

29 extracted references · 29 canonical work pages

[1]

Bukal, I

M. Bukal, I. Kukavica, L. Li, and B. Muha. A no-contact result for a plate-fluid interaction system in dimension three, 2025. arXiv:2510.09992

work page arXiv 2025
[2]

Burman, M Fernández, S

E. Burman, M Fernández, S. Frei, and F. Gerosa. A mechanically consistent model for fluid-structure interactions with contact including seepage.Comput. Methods Appl. Mech. Engrg., 392:Paper No. 114637, 28, 2022

work page 2022
[3]

Casanova, C

J. Casanova, C. Grandmont, and M. Hillairet. On an existence theory for a fluid-beam problem encompassing possible contacts.J. Éc. polytech. Math., 8:933–971, 2021

work page 2021
[4]

Cesik, M

A. Cesik, M. Kampschulte, and S. Schwarzacher. Fluid-structure interactions with navier- and full-slip boundary conditions, 2026. arXiv:2603.12030

work page arXiv 2026
[5]

Chambolle, B

A. Chambolle, B. Desjardins, M. J. Esteban, and C. Grandmont. Existence of weak solutions for the unsteady interaction of a viscous fluid with an elastic plate.J. Math. Fluid Mech., 7(3):368–404, 2005

work page 2005
[6]

C. H. A. Cheng and S. Shkoller. The interaction of the 3D Navier-Stokes equations with a moving nonlinear Koiter elastic shell.SIAM J. Math. Anal., 42(3):1094–1155, 2010

work page 2010
[7]

D.CoutandandS.Shkoller.TheinteractionbetweenquasilinearelastodynamicsandtheNavier-Stokesequations. Arch. Ration. Mech. Anal., 179(3):303–352, 2006

work page 2006
[8]

Feireisl

E. Feireisl. On the motion of rigid bodies in a viscous incompressible fluid. volume 3, pages 419–441. 2003. Dedicated to Philippe Bénilan

work page 2003
[9]

G. P. Galdi.An introduction to the mathematical theory of the Navier-Stokes equations. Springer Monographs in Mathematics. Springer, New York, second edition, 2011. Steady-state problems

work page 2011
[10]

Gérard-Varet and M

D. Gérard-Varet and M. Hillairet. Computation of the drag force on a sphere close to a wall: the roughness issue.ESAIM Math. Model. Numer. Anal., 46(5):1201–1224, 2012

work page 2012
[11]

Gérard-Varet and M

D. Gérard-Varet and M. Hillairet. Existence of weak solutions up to collision for viscous fluid-solid systems with slip.Comm. Pure Appl. Math., 67(12):2022–2075, 2014

work page 2022
[12]

The influence of boundary conditions on the contact problem in a 3D Navier-Stokes flow.J

David Gérard-Varet, Matthieu Hillairet, and Chao Wang. The influence of boundary conditions on the contact problem in a 3D Navier-Stokes flow.J. Math. Pures Appl. (9), 103(1):1–38, 2015. FINITE-TIME CONTACT: NA VIER-SLIP 33

work page 2015
[13]

Grandmont

C. Grandmont. Existence of weak solutions for the unsteady interaction of a viscous fluid with an elastic plate. SIAM J. Math. Anal., 40(2):716–737, 2008

work page 2008
[14]

Grandmont and M

C. Grandmont and M. Hillairet. Existence of global strong solutions to a beam–fluid interaction system.Arch. Ration. Mech. Anal., 220(3):1283–1333, 2016

work page 2016
[15]

Gravina, S

G. Gravina, S. Schwarzacher, O. Souček, and K. Tůma. Contactless rebound of elastic bodies in a viscous incompressible fluid.J. Fluid Mech., 942:Paper No. A34, 46, 2022

work page 2022
[16]

J. G. Heywood, R. Rannacher, and S. Turek. Artificial boundaries and flux and pressure conditions for the incompressible Navier-Stokes equations.Internat. J. Numer. Methods Fluids, 22(5):325–352, 1996

work page 1996
[17]

Kukavica, A

I. Kukavica, A. Tuffaha, and M. Ziane. Strong solutions for a fluid structure interaction system.Adv. Differential Equations, 15(3-4):231–254, 2010

work page 2010
[18]

Lengeler and M

D. Lengeler and M. Ružička. Weak solutions for an incompressible Newtonian fluid interacting with a Koiter type shell.Arch. Ration. Mech. Anal., 211(1):205–255, 2014

work page 2014
[19]

Mindrilˇ a and A

C. Mindrilˇ a and A. Roy. Existence of weak solutions for incompressible fluid-koiter shell interactions with navier slip boundary condition, 2026. arXiv:2602.20016

work page arXiv 2026
[20]

Muha and S

B. Muha and S. Čanić. Existence of a weak solution to a fluid-elastic structure interaction problem with the Navier slip boundary condition.J. Differential Equations, 260(12):8550–8589, 2016

work page 2016
[21]

Muha and S

B. Muha and S. Čanić. Existence of a weak solution to a nonlinear fluid-structure interaction problem modeling the flow of an incompressible, viscous fluid in a cylinder with deformable walls.Arch. Ration. Mech. Anal., 207(3):919–968, 2013

work page 2013
[22]

Muha and S

B. Muha and S. Čanić. A generalization of the Aubin-Lions-Simon compactness lemma for problems on moving domains.J. Differential Equations, 266(12):8370–8418, 2019

work page 2019
[23]

Neustupa and P Penel

J. Neustupa and P Penel. A weak solvability of the Navier-Stokes equation with Navier’s boundary condition around a ball striking the wall. InAdvances in mathematical fluid mechanics, pages 385–407. Springer, Berlin, 2010

work page 2010
[24]

J. A. San Martín, V. Starovoitov, and M. Tucsnak. Global weak solutions for the two-dimensional motion of several rigid bodies in an incompressible viscous fluid.Arch. Ration. Mech. Anal., 161(2):113–147, 2002

work page 2002
[25]

G. Sperone. Homogenization of the steady-state Navier-Stokes equations with prescribed flux rate or pressure drop in a perforated pipe.J. Differential Equations, 375:1–29, 2023

work page 2023
[26]

Starovoitov

V. Starovoitov. Behavior of a rigid body in an incompressible viscous fluid near a boundary. InFree boundary problems (Trento, 2002), volume 147 ofInternat. Ser. Numer. Math., pages 313–327. Birkhäuser, Basel, 2004

work page 2002
[27]

K. Tawri. A stochastic fluid-structure interaction problem with the Navier-slip boundary condition.SIAM J. Math. Anal., 56(6):7508–7544, 2024

work page 2024
[28]

Čanić, J

S. Čanić, J. Kuan, B. Muha, and K. Tawri.Deterministic and Stochastic Fluid-Structure Interaction. Advances in Mathematical Fluid Mechanics. Birkhäuser/Springer, Cham, 2025

work page 2025
[29]

Čanić, B

S. Čanić, B. Muha, and K. Tawri. Existence and regularity results for a nonlinear fluid-structure interaction problem with three-dimensional structural displacement.to appear in SIAM J. Math. Anal., 2026. preprint at arXiv:2409.06939. 1 Department of Applied Mathematics, University of W ashington, W A, USA. Email address:ktawri@uw.edu (Krutika Tawri), Nas...

work page arXiv 2026

[1] [1]

Bukal, I

M. Bukal, I. Kukavica, L. Li, and B. Muha. A no-contact result for a plate-fluid interaction system in dimension three, 2025. arXiv:2510.09992

work page arXiv 2025

[2] [2]

Burman, M Fernández, S

E. Burman, M Fernández, S. Frei, and F. Gerosa. A mechanically consistent model for fluid-structure interactions with contact including seepage.Comput. Methods Appl. Mech. Engrg., 392:Paper No. 114637, 28, 2022

work page 2022

[3] [3]

Casanova, C

J. Casanova, C. Grandmont, and M. Hillairet. On an existence theory for a fluid-beam problem encompassing possible contacts.J. Éc. polytech. Math., 8:933–971, 2021

work page 2021

[4] [4]

Cesik, M

A. Cesik, M. Kampschulte, and S. Schwarzacher. Fluid-structure interactions with navier- and full-slip boundary conditions, 2026. arXiv:2603.12030

work page arXiv 2026

[5] [5]

Chambolle, B

A. Chambolle, B. Desjardins, M. J. Esteban, and C. Grandmont. Existence of weak solutions for the unsteady interaction of a viscous fluid with an elastic plate.J. Math. Fluid Mech., 7(3):368–404, 2005

work page 2005

[6] [6]

C. H. A. Cheng and S. Shkoller. The interaction of the 3D Navier-Stokes equations with a moving nonlinear Koiter elastic shell.SIAM J. Math. Anal., 42(3):1094–1155, 2010

work page 2010

[7] [7]

D.CoutandandS.Shkoller.TheinteractionbetweenquasilinearelastodynamicsandtheNavier-Stokesequations. Arch. Ration. Mech. Anal., 179(3):303–352, 2006

work page 2006

[8] [8]

Feireisl

E. Feireisl. On the motion of rigid bodies in a viscous incompressible fluid. volume 3, pages 419–441. 2003. Dedicated to Philippe Bénilan

work page 2003

[9] [9]

G. P. Galdi.An introduction to the mathematical theory of the Navier-Stokes equations. Springer Monographs in Mathematics. Springer, New York, second edition, 2011. Steady-state problems

work page 2011

[10] [10]

Gérard-Varet and M

D. Gérard-Varet and M. Hillairet. Computation of the drag force on a sphere close to a wall: the roughness issue.ESAIM Math. Model. Numer. Anal., 46(5):1201–1224, 2012

work page 2012

[11] [11]

Gérard-Varet and M

D. Gérard-Varet and M. Hillairet. Existence of weak solutions up to collision for viscous fluid-solid systems with slip.Comm. Pure Appl. Math., 67(12):2022–2075, 2014

work page 2022

[12] [12]

The influence of boundary conditions on the contact problem in a 3D Navier-Stokes flow.J

David Gérard-Varet, Matthieu Hillairet, and Chao Wang. The influence of boundary conditions on the contact problem in a 3D Navier-Stokes flow.J. Math. Pures Appl. (9), 103(1):1–38, 2015. FINITE-TIME CONTACT: NA VIER-SLIP 33

work page 2015

[13] [13]

Grandmont

C. Grandmont. Existence of weak solutions for the unsteady interaction of a viscous fluid with an elastic plate. SIAM J. Math. Anal., 40(2):716–737, 2008

work page 2008

[14] [14]

Grandmont and M

C. Grandmont and M. Hillairet. Existence of global strong solutions to a beam–fluid interaction system.Arch. Ration. Mech. Anal., 220(3):1283–1333, 2016

work page 2016

[15] [15]

Gravina, S

G. Gravina, S. Schwarzacher, O. Souček, and K. Tůma. Contactless rebound of elastic bodies in a viscous incompressible fluid.J. Fluid Mech., 942:Paper No. A34, 46, 2022

work page 2022

[16] [16]

J. G. Heywood, R. Rannacher, and S. Turek. Artificial boundaries and flux and pressure conditions for the incompressible Navier-Stokes equations.Internat. J. Numer. Methods Fluids, 22(5):325–352, 1996

work page 1996

[17] [17]

Kukavica, A

I. Kukavica, A. Tuffaha, and M. Ziane. Strong solutions for a fluid structure interaction system.Adv. Differential Equations, 15(3-4):231–254, 2010

work page 2010

[18] [18]

Lengeler and M

D. Lengeler and M. Ružička. Weak solutions for an incompressible Newtonian fluid interacting with a Koiter type shell.Arch. Ration. Mech. Anal., 211(1):205–255, 2014

work page 2014

[19] [19]

Mindrilˇ a and A

C. Mindrilˇ a and A. Roy. Existence of weak solutions for incompressible fluid-koiter shell interactions with navier slip boundary condition, 2026. arXiv:2602.20016

work page arXiv 2026

[20] [20]

Muha and S

B. Muha and S. Čanić. Existence of a weak solution to a fluid-elastic structure interaction problem with the Navier slip boundary condition.J. Differential Equations, 260(12):8550–8589, 2016

work page 2016

[21] [21]

Muha and S

B. Muha and S. Čanić. Existence of a weak solution to a nonlinear fluid-structure interaction problem modeling the flow of an incompressible, viscous fluid in a cylinder with deformable walls.Arch. Ration. Mech. Anal., 207(3):919–968, 2013

work page 2013

[22] [22]

Muha and S

B. Muha and S. Čanić. A generalization of the Aubin-Lions-Simon compactness lemma for problems on moving domains.J. Differential Equations, 266(12):8370–8418, 2019

work page 2019

[23] [23]

Neustupa and P Penel

J. Neustupa and P Penel. A weak solvability of the Navier-Stokes equation with Navier’s boundary condition around a ball striking the wall. InAdvances in mathematical fluid mechanics, pages 385–407. Springer, Berlin, 2010

work page 2010

[24] [24]

J. A. San Martín, V. Starovoitov, and M. Tucsnak. Global weak solutions for the two-dimensional motion of several rigid bodies in an incompressible viscous fluid.Arch. Ration. Mech. Anal., 161(2):113–147, 2002

work page 2002

[25] [25]

G. Sperone. Homogenization of the steady-state Navier-Stokes equations with prescribed flux rate or pressure drop in a perforated pipe.J. Differential Equations, 375:1–29, 2023

work page 2023

[26] [26]

Starovoitov

V. Starovoitov. Behavior of a rigid body in an incompressible viscous fluid near a boundary. InFree boundary problems (Trento, 2002), volume 147 ofInternat. Ser. Numer. Math., pages 313–327. Birkhäuser, Basel, 2004

work page 2002

[27] [27]

K. Tawri. A stochastic fluid-structure interaction problem with the Navier-slip boundary condition.SIAM J. Math. Anal., 56(6):7508–7544, 2024

work page 2024

[28] [28]

Čanić, J

S. Čanić, J. Kuan, B. Muha, and K. Tawri.Deterministic and Stochastic Fluid-Structure Interaction. Advances in Mathematical Fluid Mechanics. Birkhäuser/Springer, Cham, 2025

work page 2025

[29] [29]

Čanić, B

S. Čanić, B. Muha, and K. Tawri. Existence and regularity results for a nonlinear fluid-structure interaction problem with three-dimensional structural displacement.to appear in SIAM J. Math. Anal., 2026. preprint at arXiv:2409.06939. 1 Department of Applied Mathematics, University of W ashington, W A, USA. Email address:ktawri@uw.edu (Krutika Tawri), Nas...

work page arXiv 2026