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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…

Analysis of PDEs · Mathematics 2026-04-09 Krutika Tawri , Nash Ward

In this paper, we study a free boundary problem for compressible spherically symmetric Navier-Stokes equations with a gravitational force and degenerate viscosity coefficients. Under certain assumptions that imposed on the initial data, we…

Analysis of PDEs · Mathematics 2007-05-23 Mingjun Wei , Ting Zhang , Daoyuan Fang

We consider a non-linear system modelling the dynamics of a linearly elastic body immersed in an incompressible viscous fluid, without damping on the elastic part. We prove local existence of strong solutions and global existence and…

Analysis of PDEs · Mathematics 2025-08-20 Karoline Disser , Michelle Luckas

The evolution of the interface separating a conduit of light, viscous fluid rising buoyantly through a heavy, more viscous, exterior fluid at small Reynolds numbers is governed by the interplay between nonlinearity and dispersion. Previous…

Fluid Dynamics · Physics 2015-06-16 Nicholas K. Lowman , Mark A. Hoefer

We prove that there exists a~large-data and global-in-time weak solution to a~system of partial differential equations describing an unsteady flow of an incompressible heat-conducting rate-type viscoelastic stress-diffusive fluid filling up…

Analysis of PDEs · Mathematics 2025-04-18 Michal Bathory , Miroslav Bulíček , Josef Málek

Here, we consider the elasto-capillary fluid-structure interaction problem studied in Bhopalam, Bueno & Gomez (2022), i.e., three immiscible fluids in contact with an elastic solid. In this article, we show that the solution of this…

Analysis of PDEs · Mathematics 2024-10-10 Sthavishtha R. Bhopalam , Hector Gomez

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

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

In this paper we consider a slab of viscous incompressible fluid bounded above by a free boundary, bounded below by a flat rigid interface, and acted on by gravity. The unique equilibrium is a flat slab of quiescent fluid. It is well-known…

Analysis of PDEs · Mathematics 2018-06-12 Ian Tice , Samuel Zbarsky

This paper is concerned with the free boundary value problem for multi-dimensional Navier-Stokes equations with density-dependent viscosity where the flow density vanishes continuously across the free boundary. A local (in time) existence…

Analysis of PDEs · Mathematics 2015-03-24 Jian Liu

We consider the compressible Navier-Stokes-Fourier system on time-dependent domains with prescribed motion of the boundary, supplemented with slip boundary conditions for the velocity. Assuming that the pressure can be decomposed into an…

Analysis of PDEs · Mathematics 2015-11-17 Ondrej Kreml , Vaclav Macha , Sarka Necasova , Aneta Wroblewska-Kaminska

We study a thermodynamically consistent diffuse interface model that describes the motion of a two-phase flow of two viscous incompressible Newtonian fluids with unmatched densities and a soluble surfactant in a bounded domain of two or…

Analysis of PDEs · Mathematics 2026-01-13 Bohan Ouyang , Maurizio Grasselli , Hao Wu

We address a system of equations modeling an incompressible fluid interacting with an elastic body. We prove the local existence when the initial velocity belongs to the space $H^{1.5+\epsilon}$ and the initial structure velocity is in…

Analysis of PDEs · Mathematics 2023-12-29 Igor Kukavica , Linfeng Li , Amjad Tuffaha

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

In this paper, we investigate the dynamics of an incompressible viscous Navier-Stokes fluid evolving above a one-dimensional flat surface. The fluid is subject to a uniform gravitational field and capillary forces acting along the free…

Analysis of PDEs · Mathematics 2026-02-19 Xiaoding Yang

Within the framework of continuum mechanics, the full description Of joint motion of elastic bodies and compressible viscous fluids with taking into account thermal effects is given by the system consisting of the mass, momentum, and energy…

Analysis of PDEs · Mathematics 2007-05-23 Anvarbek M. Meirmanov , Sergei A. Sazhenkov

In this paper we consider the motion of a rigid body in a viscous incompressible fluid when some Navier slip conditions are prescribed on the body's boundary. The whole `viscous incompressible fluid + rigid body' system is assumed to occupy…

Analysis of PDEs · Mathematics 2018-10-03 Marco Bravin

We study the existence of weak martingale solutions to a stochastic moving boundary problem arising from the interaction between an isentropic compressible fluid and a viscoelastic structure. In the model, we consider a three-dimensional…

Analysis of PDEs · Mathematics 2025-05-22 Jeffrey Kuan , Krutika Tawri

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

We consider several rigid bodies immersed in a viscous Newtonian fluid contained in a bounded domain in $R^3$. We introduce a new concept of dissipative weak solution of the problem based on a combination of the approach proposed by Judakov…

Analysis of PDEs · Mathematics 2026-05-29 Marco Bravin , Eduard Feireisl , Arnab Roy , Arghir Zarnescu

In this work, we derive asymptotic interface models for an elastic Muskat free boundary problem describing Darcy flow beneath an elastic membrane. In a weakly nonlinear regime of small interface steepness, we obtain nonlocal evolution…

Analysis of PDEs · Mathematics 2026-02-12 Diego Alonso-Orán , Rafael Granero-Belinchón