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Related papers: Analysis of the coupled Navier-Stokes/Biot problem

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A model is developed describing the approach to a finite-time singularity of the Navier-Stokes equations for two interacting vortices. The model is derived from a combination of the Biot-Savart law and an equation describing the evolution…

Fluid Dynamics · Physics 2018-11-21 Keith Moffatt , Yoshifumi Kimura

We show weak-strong uniqueness and stability results for the motion of a two or three dimensional fluid governed by the Navier-Stokes equation interacting with a flexible, elastic plate of Koiter type. The plate is situated at the top of…

Analysis of PDEs · Mathematics 2020-10-05 Sebastian Schwarzacher , Matthias Sroczinski

We study a hydrodynamic limit of a system of coupled kinetic and fluid equations under a strong local alignment force and a strong Brownian motion. More precisely, we consider the Vlasov-Fokker-Planck type equation and compressible…

Analysis of PDEs · Mathematics 2019-01-07 Young-Pil Choi , Jinwook Jung

We study a moving boundary value problem consisting of a viscous incompressible fluid moving and interacting with a nonlinear elastic fluid shell. The fluid motion is governed by the Navier-Stokes equations, while the fluid shell is modeled…

Analysis of PDEs · Mathematics 2007-05-23 C. H. Arthur Cheng , Daniel Coutand , Steve Shkoller

In this paper we present and analyze a fully-mixed formulation for the coupled problem arising in the interaction between a free fluid and a flow in a poroelastic medium. The flows are governed by the Stokes and Biot equations,…

Numerical Analysis · Mathematics 2021-05-25 Sergio Caucao , Tongtong Li , Ivan Yotov

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…

Analysis of PDEs · Mathematics 2023-02-13 Martin Kalousek , Sourav Mitra , Šárka Nečasová

We study the Navier--Stokes equations governing the motion of an isentropic compressible fluid in three dimensions interacting with a flexible shell of Koiter type. The latter one constitutes a moving part of the boundary of the physical…

Analysis of PDEs · Mathematics 2018-01-17 Dominic Breit , Sebastian Schwarzacher

A perfectly elastic beam is situated on top of a two dimensional fluid canister. The beam is deforming in accordance to an interaction with a Navier-Stokes fluid. Hence a hyperbolic equation is coupled to the Navier-Stokes equation. The…

Analysis of PDEs · Mathematics 2024-02-19 Sebastian Schwarzacher , Pei Su

We consider the three-dimensional fluid-structure interaction system modeling a system consisting of a viscous incompressible fluid and an elastic plate forming its moving upper boundary. The fluid is described by the incompressible…

Analysis of PDEs · Mathematics 2025-12-12 Mario Bukal , Igor Kukavica , Linfeng Li , Boris Muha

We study the long-time dynamics of a non-autonomous coupled system consisting of the 3D linearized Na\-vier--Stokes equations and nonlinear elasticity equations. We show that this problem generates a process on time-dependent spaces…

Dynamical Systems · Mathematics 2018-08-10 Tamara Fastovska

We approximate a two--phase model by the compressible Navier-Stokes equations with a singular pressure term. Up to a subsequence, these solutions are shown to converge to a global weak solution of the compressible system with the congestion…

Analysis of PDEs · Mathematics 2014-10-03 Charlotte Perrin , Ewelina Zatorska

We consider the interaction of a compressible fluid with a flexible plate in two space dimensions. The fluid is described by the Navier--Stokes equations in a domain that is changing in accordance with the motion of the structure. The…

Analysis of PDEs · Mathematics 2024-11-05 Dominic Breit , Arnab Roy

This article considers fluid structure interaction describing the motion of a fluid contained in a porous medium. The fluid is modelled by Navier-Stokes equations and the coupling between fluid and the porous medium is described by the…

Analysis of PDEs · Mathematics 2025-01-17 Tim Binz , Matthias Hieber , Arnab Roy

Under the action of a time-periodic external forces we prove the existence of at least one time-periodic weak solution for the interaction between a three-dimensional incompressible fluid, governed by the Navier- Stokes equation and a two…

Analysis of PDEs · Mathematics 2022-04-08 Claudiu Mîndrilă , Sebastian Schwarzacher

We aim at the stability of time-dependent motions, such as time-periodic ones, of a rigid body in a viscous fluid filling the exterior to it in 3D. The fluid motion obeys the incompressible Navier-Stokes system, whereas the motion of the…

Analysis of PDEs · Mathematics 2024-02-21 Toshiaki Hishida

We study a fluid-structure interaction problem between a viscous incompressible fluid and an elastic beam with fixed endpoints in a static setting. The 3D fluid domain is bounded, nonsmooth and non simply connected, the fluid is modeled by…

Analysis of PDEs · Mathematics 2026-01-30 Vincenzo Bianca , Edoardo Bocchi , Filippo Gazzola

We consider the compressible (barotropic) Navier-Stokes system on time-dependent domains, supplemented with slip boundary conditions. Our approach is based on penalization of the boundary behaviour, viscosity, and the pressure in the weak…

Analysis of PDEs · Mathematics 2015-04-01 Eduard Feireisl , Ondřej Kreml , Šárka Nečasová , Jiří Neustupa , Jan Stebel

In this paper we consider a fluid-structure interaction problem given by the steady Navier Stokes equations coupled with linear elasticity taken from [Lasiecka, Szulc, and Zochoswki, Nonl. Anal.: Real World Appl., 44, 2018]. An elastic body…

Optimization and Control · Mathematics 2021-09-07 Michael Hintermüller , Axel Kröner

We study a stationary 3D/2D fluid-structure interaction problem between an elastic structure described by the linear plate equation and a fluid described by the compressible Navier-Stokes equations with hard-sphere pressure and…

Analysis of PDEs · Mathematics 2026-03-30 Boris Muha , Šárka Nečasová , Milan Pokorný , Srđan Trifunović , Justin T. Webster

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…

Analysis of PDEs · Mathematics 2023-10-10 Helmut Abels , Yadong Liu