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In this paper, the system of particles coupled with fluid is considered. The particles are described by a Vlasov equation, and the fluid is governed by a forced Navier-Stokes equations. The interaction with fluid phase governed by…

Analysis of PDEs · Mathematics 2012-11-28 Cheng Yu

We introduce and analyze a space-time least-squares method associated to the unsteady Navier-Stokes system. Weak solution in the two dimensional case and regular solution in the three dimensional case are considered. From any initial guess,…

Optimization and Control · Mathematics 2019-09-12 Jerome Lemoine , Arnaud Munch

We study a nonlinear, moving boundary fluid-structure interaction problem between an incompressible, viscous Newtonian fluid, modeled by the 2D Navier-Stokes equations, and an elastic structure modeled by the shell or plate equations. The…

Analysis of PDEs · Mathematics 2016-03-07 Boris Muha , Suncica Canic

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 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 study a nonlinear interaction problem between a thermoelastic shell and a heat-conducting fluid. The shell is governed by linear thermoelasticity equations and encompasses a time-dependent domain which is filled with a…

Analysis of PDEs · Mathematics 2022-03-01 Václav Mácha , Boris Muha , Šárka Nečasová , Arnab Roy , Srđan Trifunović

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 present a system of Navier-Stokes type that describes the dynamics of several spherical bubbles of gas in a liquid. It is derived from a more complete model, where the bubbles are seen as inclusions of gas of homogeneous barotropic…

Analysis of PDEs · Mathematics 2025-07-30 Cosmin Burtea , David Gérard-Varet

We prove existence of weak solutions for a diffuse interface model for the flow of two viscous incompressible Newtonian fluids in a bounded domain in two and three space dimensions. In contrast to previous works, we study a new model…

Analysis of PDEs · Mathematics 2015-06-03 Helmut Abels , Daniel Depner , Harald Garcke

We discuss the applicability of a unified hyperbolic model for continuum fluid and solid mechanics to modeling non-Newtonian flows and in particular to modeling the stress-driven solid-fluid transformations in flows of viscoplastic fluids,…

In this paper, we consider two systems modelling the evolution of a rigid body in an incompressible fluid in a bounded domain of the plane. The first system corresponds to an inviscid fluid driven by the Euler equation whereas the other one…

Analysis of PDEs · Mathematics 2024-12-30 Olivier Glass , Franck Sueur

At the molecular level fluid motions are, by first principles, described by time reversible laws. On the other hand, the coarse grained macroscopic evolution is suitably described by the Navier-Stokes equations, which are inherently…

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

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 prove the existence of martingale solutions to a stochastic fluid-structure interaction problem involving a viscous, incompressible fluid flow, modeled by the Navier-Stokes equations, through a deformable elastic tube modeled by…

Analysis of PDEs · Mathematics 2024-02-22 Krutika Tawri

We propose and analyze unfitted finite element approximations for the two-phase incompressible Navier--Stokes flow in an axisymmetric setting. The discretized schemes are based on an Eulerian weak formulation for the Navier--Stokes equation…

Numerical Analysis · Mathematics 2023-09-12 Harald Garcke , Robert Nürnberg , Quan Zhao

We consider evolution (non-stationary) space-periodic solutions to the $n$-dimensional non-linear Navier-Stokes equations of anisotropic fluids with the viscosity coefficient tensor variable in space and time and satisfying the relaxed…

Analysis of PDEs · Mathematics 2024-02-09 Sergey E. Mikhailov

Governing equations of motion for a viscous incompressible material surface are derived from the balance laws of continuum mechanics. The surface is treated as a time-dependent smooth orientable manifold of codimension one in an ambient…

Mathematical Physics · Physics 2018-10-10 Thomas Jankuhn , Maxim A. Olshanskii , Arnold Reusken

This paper studies global existence, hydrodynamic limit, and large-time behavior of weak solutions to a kinetic flocking model coupled to the incompressible Navier-Stokes equations. The model describes the motion of particles immersed in a…

Analysis of PDEs · Mathematics 2013-11-25 J. A. Carrillo , Y. -P. Choi , T. K. Karper