English
Related papers

Related papers: Two-phase flows with bulk-surface interaction: the…

200 papers

We prove that there exists a weak solution to a system governing an unsteady flow of a viscoelastic fluid in three dimensions, for arbitrarily large time interval and data. The fluid is described by the incompressible Navier-Stokes…

Analysis of PDEs · Mathematics 2020-07-22 Michal Bathory , Miroslav Bulíček , Josef Málek

We investigate a fluid-structure interaction system in which the dynamics of the fluid is described by the compressible Navier-Stokes equations, while the elastic structure is modeled by a damped plate equation. The fluid evolves in a…

Analysis of PDEs · Mathematics 2026-04-20 Kuntal Bhandari , Imene Aicha Djebour , Šárka Nečasová

A novel thermodynamically consistent diffuse interface model is derived for compressible electrolytes with phase transitions. The fluid mixtures may consist of N constituents with the phases liquid and vapor, where both phases may coexist.…

Analysis of PDEs · Mathematics 2014-11-13 Wolfgang Dreyer , Jan Giesselmann , Christiane Kraus

We consider weak solutions for a diffuse interface model of two non-Newtonian viscous, incompressible fluids of power-law type in the case of different densities in a bounded, sufficiently smooth domain. This leads to a coupled system of a…

Analysis of PDEs · Mathematics 2017-01-03 Helmut Abels , Dominic Breit

In this work, a thermodynamically consistent and conservative diffuse-interface model for gas-liquid-solid multiphase flows is proposed. In this model, a novel free energy for the gas-liquid-solid multiphase flows is established according…

Fluid Dynamics · Physics 2025-04-09 Chengjie Zhan , Xi Liu , Zhenhua Chai , Baochang Shi

In this article, a suite of physically inconsistent properties of the Navier-Stokes equations, associated with the lack of mass diffusion and the definition of velocity, are presented. We show that these inconsistencies are consequences of…

Fluid Dynamics · Physics 2018-01-09 Magnus Svärd

The Cahn-Hilliard equation is the most common model to describe phase separation processes of a mixture of two components. For a better description of short-range interactions of the material with the solid wall, various dynamic boundary…

Analysis of PDEs · Mathematics 2020-10-20 Harald Garcke , Patrik Knopf

The heat conducting compressible viscous flows are governed by the Navier-Stokes-Fourier (NSF) system. In this paper, we study the NSF system accomplished by the Newton law of cooling for the heat transfer at the boundary. On one part of…

Analysis of PDEs · Mathematics 2021-11-23 Luisa Consiglieri

We study the full Navier--Stokes--Fourier system governing the motion of a general viscous, heat-conducting, and compressible fluid subject to stochastic perturbation. The system is supplemented with non-homogeneous Neumann boundary…

Analysis of PDEs · Mathematics 2021-02-09 Dominic Breit , Eduard Feireisl , Martina Hofmanová

This paper concerns a diffuse interface model for the flow of two incompressible viscoelastic fluids in a bounded domain. More specifically, the fluids are assumed to be macroscopically immiscible, but with a small transition region, where…

Analysis of PDEs · Mathematics 2024-11-15 Yadong Liu , Dennis Trautwein

The two-phase Navier-Stokes Cahn-Hilliard (NSCH) mixture model is a key framework for simulating multiphase flows with non-matching densities. Developing fully discrete, energy-stable schemes for this model remains challenging, due to the…

Numerical Analysis · Mathematics 2026-02-05 Aaron Brunk , Marco F. P. ten Eikelder

Over the past few decades, numerous N-phase incompressible diffuse-interface flow models with non-matching densities have been proposed. Despite aiming to describe the same physics, these models are generally distinct, and an overarching…

Fluid Dynamics · Physics 2025-04-01 M. F. P. ten Eikelder

In this article we prove the global existence of weak solutions for a diffuse interface model in a bounded domain (both in 2D and 3D) involving incompressible magnetic fluids with unmatched densities. The model couples the incompressible…

Analysis of PDEs · Mathematics 2021-06-09 Martin Kalousek , Sourav Mitra , Anja Schlömerkemper

A kinetic-fluid model describing the evolutions of disperse two-phase flows is considered. The model consists of the Vlasov-Fokker-Planck equation for the particles (disperse phase) coupled with the compressible Navier-Stokes equations for…

Analysis of PDEs · Mathematics 2017-04-06 Fucai Li , Yanmin Mu , Dehua Wang

We prove the existence of a weak solution to the compressible Navier--Stokes system with singular pressure that explodes when density achieves its congestion level. This is a quantity whose initial value evolves according to the transport…

Analysis of PDEs · Mathematics 2022-02-09 Milan Pokornyý , Aneta Wróblewska-Kamińska , Ewelina Zatorska

In this paper we derive a class of thermodynamically consistent diffuse-interface mixture models of incompressible multicomponent fluids. The class of mixture models is fully compatible with the continuum theory of mixtures. The resulting…

Fluid Dynamics · Physics 2023-02-21 M. ten Eikelder , K. van der Zee , D. Schillinger

We show that molecular dynamics simulations can furnish useful boundary conditions at a solid surface bounding a two-component fluid. In contrast to some previous reports, convective-diffusive flow is consistent with continuum equations…

Soft Condensed Matter · Physics 2009-11-07 Colin Denniston , Mark O. Robbins

We consider the Cahn--Hilliard/Navier--Stokes system with non-degenerate mobility in the space-periodic case, describing the flow of two viscous immiscible and incompressible Newtonian fluids with matched densities. We identify sufficient…

Analysis of PDEs · Mathematics 2024-08-06 Stefanos Georgiadis

We consider a diffuse-interface model for two-phase incompressible viscous flows with a soluble surfactant in a bounded porous medium. This hydrodynamic system consists of a Darcy--Forchheimer equation for the seepage velocity…

Analysis of PDEs · Mathematics 2026-03-24 Maurizio Grasselli , Bohan Ouyang , Andrea Poiatti , Hao Wu

The aim of this article is to justify mathematically, in the two-dimensional periodic setting, a generalization of a two-phase model with pressure dependent viscosity first proposed by A. Lefebvre-Lepot and B. Maury to describe a system in…

Analysis of PDEs · Mathematics 2015-08-24 Charlotte Perrin