English
Related papers

Related papers: A Banach space formulation for the fully dynamic N…

200 papers

We consider systems of particles coupled with fluids. The particles are described by the evolution of their density, and the fluid is described by the Navier-Stokes equations. The particles add stress to the fluid and the fluid carries and…

Analysis of PDEs · Mathematics 2009-11-11 Peter Constantin , Charles Fefferman , Edriss Titi , Arghir Zarnescu

We consider the system of partial differential equations governing two-dimensional flows of a robust class of viscoelastic rate-type fluids with stress diffusion, involving a general objective derivative. The studied system generalizes the…

Analysis of PDEs · Mathematics 2022-06-08 Miroslav Bulíček , Josef Málek , Casey Rodriguez

We show the existence of weak solutions to the fluid-structure interaction problem of a largely deforming viscoelastic bulk solid with a viscous fluid governed by the incompressible Navier-Stokes equations. In contrast to previous works,…

Analysis of PDEs · Mathematics 2026-03-13 Antonín Češík , Malte Kampschulte , Sebastian Schwarzacher

We prove the existence of finite-energy weak solutions to a regularized three-dimensional fluid-structure interaction (FSI) problem involving an incompressible, viscous, Newtonian fluid and a multilayered poro(visco)elastic structure. The…

Analysis of PDEs · Mathematics 2025-08-21 Felix Brandt , Sunčica Čanić , Boris Muha

Fluid flows in coupled systems consisting of a free-flow region and the adjacent porous medium appear in a variety of environmental settings and industrial applications. In many applications, fluid flow is non-parallel to the fluid-porous…

Analysis of PDEs · Mathematics 2021-04-07 Elissa Eggenweiler , Marco Discacciati , Iryna Rybak

The stationary Navier--Stokes--Cahn--Hilliard equations are considered, governing the motion of a compressible, two-phase fluid mixture with a diffuse interface. The free energy density in this paper has a singular logarithmic…

Analysis of PDEs · Mathematics 2026-05-05 Zhilei Liang , Sen Liu , Jiangyu Shuai , Dehua Wang

Detailed understanding of the coupling between fluid flow and solid deformation in porous media is crucial for the development biomedical devices and novel energy technologies relating to a wide range of geological and biological processes.…

Fluid Dynamics · Physics 2021-09-22 Francisco J. Carrillo

In this paper, we investigate a system coupled by nonhomogeneous incompressible Navier-Stokes equations and Allen-Cahn equations describing a diffuse interface for two-phase flow of viscous fluids with different densities in a bounded…

Analysis of PDEs · Mathematics 2025-03-06 Yinghua Li , Wenlin Ye

The present article introduces, mathematically analyzes, and numerically validates a new weak Galerkin (WG) mixed-FEM based on Banach spaces for the stationary Navier--Stokes equation in pseudostress-velocity formulation. More precisely, a…

Numerical Analysis · Mathematics 2024-02-05 Zeinab Gharibi , Mehdi Dehghan

Physically consistent coupling conditions at the fluid-porous interface with correctly determined effective parameters are necessary for accurate modeling and simulation of various applications. To describe single-fluid-phase flows in…

Fluid Dynamics · Physics 2022-05-25 Paula Strohbeck , Elissa Eggenweiler , Iryna Rybak

In this paper we investigate the stress concentration problem that occurs when two convex rigid particles are closely immersed in a fluid flow. The governing equations for the fluid flow are the stationary incompressible Navier-Stokes…

Analysis of PDEs · Mathematics 2024-11-26 Haigang Li , Peihao Zhang

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

We study a general Navier-Stokes-Cahn-Hilliard-Boussinesq system that describes the motion of a mixture of two incompressible Newtonian fluids with thermo-induced Marangoni effects. The Cahn-Hilliard dynamics of the binary mixture is…

Analysis of PDEs · Mathematics 2024-08-13 Lingxi Chen

We perform linear and nonlinear stability analysis for thermal convection in a fluid overlying a saturated porous medium. We use a coupled system, with the Navier-Stokes equations and Darcy's equation governing the free-flow and the porous…

Fluid Dynamics · Physics 2019-07-08 M. McCurdy , M. N. J. Moore , X. Wang

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

In this paper we present a hybridizable discontinuous Galerkin method for the time-dependent Navier-Stokes equations coupled to the quasi-static poroelasticity equations via interface conditions. We determine a bound on the data that…

Numerical Analysis · Mathematics 2023-08-31 Aycil Cesmelioglu , Jeonghun J. Lee , Sander Rhebergen

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

In this paper, we construct and analyze new first- and second-order implicit-explicit (IMEX) schemes for the unsteady Navier-Stokes-Darcy model to describe the coupled free flow-porous media system, which is based on the scalar auxiliary…

Numerical Analysis · Mathematics 2024-05-21 Xinhui Wang , Xu Guo , Xiaoli Li

In this paper, an a priori estimate of weak solutions to the mixed Navier-Stokes/Darcy model with Beavers-Joseph-Saffman's interface condition and the existence of a weak solution are established without the small data and/or the large…

Analysis of PDEs · Mathematics 2017-01-05 Yanren Hou , Haibiao Zheng

We analyze a diffuse interface model that describes the dynamics of incompressible two-phase flows influenced by interactions with a soluble chemical substance, encompassing the chemotaxis effect, mass transport, and reactions. In the…

Analysis of PDEs · Mathematics 2026-01-13 Andrea Giorgini , Jingning He , Hao Wu