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A Cahn-Hilliard-Navier-Stokes system for two-phase flow on an evolving surface with non-matched densities is derived using methods from rational thermodynamics. For a Cahn-Hilliard energy with a singular (logarithmic) potential short time…

Analysis of PDEs · Mathematics 2025-11-18 Helmut Abels , Harald Garcke , Andrea Poiatti

We study a diffuse-interface model for thermally driven phase separation in viscous incompressible mixtures. The system couples a convective Cahn-Hilliard equation for the order parameter with a Stokes subsystem for the velocity-pressure…

Analysis of PDEs · Mathematics 2026-04-24 Maria Deliyianni , Boris Muha , Andrej Novak

We derive a thermodynamically consistent model, which describes the time evolution of a two-phase flow in an evolving domain. The movement of the free boundary of the domain is driven by the velocity field of the mixture in the bulk, which…

Analysis of PDEs · Mathematics 2026-04-29 Patrik Knopf , Yadong Liu

The incompressible Navier-Stokes equations coupled to the Maxwell-Stefan relations for the molar fluxes are analyzed in bounded domains with no-flux boundary conditions. The system models the dynamics of a multicomponent gaseous mixture…

Analysis of PDEs · Mathematics 2013-10-15 Xiuqing Chen , Ansgar Jüngel

We consider a general compressible viscous and heat conducting fluid confined between two parallel plates and heated from the bottom. The time evolution of the fluid is described by the Navier--Stokes--Fourier system considered in the…

Analysis of PDEs · Mathematics 2023-11-21 Peter Bella , Eduard Feireisl , Florian Oschmann

We study a Cahn--Hilliard two-phase model describing the flow of two viscoelastoplastic fluids, which arises in geodynamics. A phase-field variable indicates the proportional distribution of the two fluids in the mixture. The motion of the…

Analysis of PDEs · Mathematics 2025-10-01 Fan Cheng , Robert Lasarzik , Marita Thomas

The second entropy theory for non-equilibrium thermodynamics is used to show that the optimum structure or pattern of a time-dependent system corresponds to the maximum entropy. A formula for the total entropy of convective heat flow is…

Statistical Mechanics · Physics 2012-09-11 Phil Attard

We consider a scaled Navier--Stokes--Fourier system describing the motion of a compressible, heat-conducting, viscous fluid driven by inhomogeneous boundary temperature distribution together with the gravitational force of a massive object…

Analysis of PDEs · Mathematics 2024-10-02 Francesco Fanelli , Eduard Feireisl

We consider a flow of non-Newtonian heat conducting incompressible fluid in a bounded domain subjected to the homogeneous Dirichlet boundary condition for the velocity field and the spatially inhomogeneous Dirichlet boundary condition for…

Analysis of PDEs · Mathematics 2022-10-12 Anna Abbatiello , Miroslav Bulíček , Petr Kaplický

Interactions between an evolving solid and inviscid flow can result in substantial computational complexity, particularly in circumstances involving varied boundary conditions between the solid and fluid phases. Examples of such…

Fluid Dynamics · Physics 2022-09-30 Emma M. Schmidt , J. Matt Quinlan , Brandon Runnels

In this article, we study the behavior of the Abels-Garcke-Gr\"un Navier-Stokes-Cahn-Hilliard diffuse-interface model for binary-fluid flows, as the diffuse-interface thickness passes to zero. We consider this so-called sharp-interface…

Numerical Analysis · Mathematics 2023-01-05 T. H. B. Demont , S. K. F. Stoter , E. H. van Brummelen

We propose a variant of the $\theta$-scheme for diffuse interface models for two-phase flow, together with three new linearization techniques for the surface tension. These involve either additional stabilizing force terms, or a fully…

Numerical Analysis · Mathematics 2014-03-05 Sebastian Aland

A novel numerical scheme including time and spatial discretization is offered for coupled Cahn-Hilliard and Navier-Stokes governing equation sys-tem in this paper. Variable densities and viscosities are considered in the nu-merical scheme.…

Computational Physics · Physics 2018-05-25 Xiaoyu Feng , Jisheng Kou , Shuyu Sun

In this paper, we consider the heat-conducting compressible self-gravitating fluids in time-dependent domains, which typically describe the motion of viscous gaseous stars. The flow is governed by the 3-D Navier-Stokes-Fourier-Poisson…

Analysis of PDEs · Mathematics 2024-01-18 Kuntal Bhandari , Bingkang Huang , Šárka Nečasová

A multispecies diffuse interface model is formulated in a fluctuating hydrodynamics framework for the purpose of simulating surfactant interfaces at the nanoscale. The model generalizes previous work to ternary mixtures, employing a…

Fluid Dynamics · Physics 2025-08-26 John B. Bell , Andrew Nonaka , Alejandro L. Garcia

We consider the Navier-Stokes-Fourier-Poisson system driven by an inhomogeneous temperature distribution on the boundary of an exterior fluid domain. We impose the finite mass constraint, positive far field condition for the temperature as…

Analysis of PDEs · Mathematics 2024-05-14 Nilasis Chaudhuri , Eduard Feireisl , Ewelina Zatorska , Boguslaw Zegarlinski

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 consider a kinetic model of two species of particles interacting with a reservoir at fixed temperature, described by two coupled Vlasov-Fokker-Plank equations. We prove that in the diffusive limit the evolution is described by a…

Statistical Mechanics · Physics 2015-06-25 Guido Manzi , Rossana Marra

The derivation of shallow water models from Navier-Stokes equations is revisited yielding a class of two-layer shallow water models.An improved velocity profile is proposed, based on the superposition of an ideal fluid and a viscous layer…

Analysis of PDEs · Mathematics 2018-06-11 François James , Pierre-Yves Lagrée , Hoang-Minh Le , Mathilde Legrand

The existence of large-data weak solutions to a steady compressible Navier-Stokes-Fourier system for chemically reacting fluid mixtures is proved. General free energies are considered satisfying some structural assumptions, with a pressure…

Analysis of PDEs · Mathematics 2024-06-19 Miroslav Buliček , Ansgar Jüngel , Milan Pokorný , Nicola Zamponi