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Related papers: Uniqueness of Weak Solutions for Biot-Stokes Inter…

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We study a fluid-poroelasticity interaction (FPSI) problem coupling the unsteady Stokes equations with the fully dynamic Biot system. A major challenge in such problems is to design partitioned schemes that remain robust in locking-related…

Numerical Analysis · Mathematics 2026-04-13 Wenlong He , Thomas Wick , Xiaohe Yue , Jiwei Zhang , Haibiao Zheng

We consider the flow of two viscous and incompressible fluids within a bounded domain modeled by means of a two-phase Navier-Stokes system. The two fluids are assumed to be immiscible, meaning that they are separated by an interface. With…

Analysis of PDEs · Mathematics 2022-08-24 Sebastian Hensel , Alice Marveggio

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 prove existence of weak solutions to a diffuse interface model describing the flow of a fluid through a deformable porous medium consisting of two phases. The system non-linearly couples Biot's equations for poroelasticity, including…

Analysis of PDEs · Mathematics 2024-08-27 Helmut Abels , Harald Garcke , Jonas Haselböck

We study the interaction between incompressible viscous fluids and multilayered elastic structures in a 3D/2D/3D framework, where a 3D fluid interacts with a 2D thin elastic layer, coupled to a 3D thick elastic solid. The system is driven…

Analysis of PDEs · Mathematics 2025-01-14 Claudiu Mîndrilă , Arnab Roy

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 investigate the existence of weak solutions to a certain system of partial differential equations, modelling the behaviour of a compressible non-Newtonian fluid for small Reynolds number. We construct the weak solutions despite the lack…

Analysis of PDEs · Mathematics 2023-05-24 Milan Pokorný , Maja Szlenk

We study a new fully averaged poroelastic Kirchhoff plate model coupled with the flow of an incompressible, viscous fluid governed by the time-dependent Stokes equations. The fully averaged formulation offers several advantages over the…

Analysis of PDEs · Mathematics 2026-05-20 Felix Brandt , Sunčica Čanić , Andrew Scharf , Josip Tambača

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

In this paper we advance the analysis of discretizations for a fluid-structure interaction model of the monolithic coupling between the free flow of a viscous Newtonian fluid and a deformable porous medium separated by an interface. A…

Numerical Analysis · Mathematics 2023-06-27 Wietse M. Boon , Martin Hornkjøl , Miroslav Kuchta , Kent-Andre Mardal , Ricardo Ruiz-Baier

We analyze a diffuse interface model that describes the dynamics of incompressible two-phase flows with chemotaxis effect. The PDE system couples a Navier-Stokes equation for the fluid velocity, a convective Cahn-Hilliard equation for the…

Analysis of PDEs · Mathematics 2020-02-04 Jingning He

We study the unsteady incompressible Navier-Stokes equations in three dimensions interacting with a non-linear flexible shell of Koiter type. This leads to a coupled system of non-linear PDEs where the moving part of the boundary is an…

Analysis of PDEs · Mathematics 2022-11-15 Boris Muha , Sebastian Schwarzacher

We propose a partitioned method for the monolithic formulation of the Stokes-Biot system that incorporates Lagrange multipliers enforcing the interface conditions. The monolithic system is discretized using finite elements, and we establish…

Numerical Analysis · Mathematics 2026-01-21 Amy de Castro , Hyesuk Lee

In this article the question on uniqueness of weak solution of the incompressible Navier-Stokes Equations in the 3-dimensional case is studied. Here the investigation is carried out with use of another approach. The uniqueness of velocity…

Analysis of PDEs · Mathematics 2020-09-29 Kamal N. Soltanov

This article studies the uniqueness of the weak solution of the incompressible Navier-Stokes Equations in the 3-dimensional case. Here, the investigation is provided using two different approaches. The first (the main) result is obtained…

Analysis of PDEs · Mathematics 2024-05-20 Kamal N. Soltanov

We develop and analyze a splitting method for fluid-poroelastic structure interaction. The fluid is described using the Stokes equations and the poroelastic structure is described using the Biot equations. The transmission conditions on the…

Numerical Analysis · Mathematics 2024-09-30 Aashi Dalal , Rebecca Durst , Annalisa Quaini , Ivan Yotov

We consider the problem of a 3D-3D-2D mutually coupled solute-solvent-structure three-states system. This describes the interaction of a flexible structure with a polymeric fluid of classical Oldroyd-B type without centre-of-mass diffusion.…

Analysis of PDEs · Mathematics 2025-10-16 Prince Romeo Mensah

In this paper we investigate the existence of solutions and their weak-strong uniqueness property for a PDE system modelling damage in viscoelastic materials. In fact, we address two solution concepts, weak and strong solutions. For the…

Analysis of PDEs · Mathematics 2024-09-04 Robert Lasarzik , Elisabetta Rocca , Riccarda Rossi

We consider a system of nonlinear equations which can be reduced to a degenerate parabolic equation. In the case $x\in\bR^2$ we obtained necessary conditions for the existence of a weakly singular solution of heat wave type…

Mathematical Physics · Physics 2007-05-23 Georgii A. Omel'yanov

We consider a poromechanics model including frictionless contact mechanics. The resulting model consists of the Biot equations with contact boundary conditions leading to a variational inequality modelling mechanical deformations coupled to…

Numerical Analysis · Mathematics 2024-07-19 Tameem Almani , Kundan Kumar