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We investigate the initial-value problem for the incompressible tangential Navier-Stokes equation with variable viscosity on a given two-dimensional surface without boundary. Existence of global weak and strong solutions under inhomogeneous…

Analysis of PDEs · Mathematics 2024-12-10 Andrea Poiatti , Ulisse Stefanelli

We study a diffuse-interface model for a binary incompressible mixture in a periodically perforated porous medium, described by a time-dependent Navier-Stokes-Cahn-Hilliard (NSCH) system posed on the pore domain…

Analysis of PDEs · Mathematics 2026-03-17 Amartya Chakrabortty , Haradhan Dutta , Hari Shankar Mahato

This paper addresses the three-dimensional Navier-Stokes equations for an incompressible fluid whose density is permitted to be inhomogeneous. We establish a theorem of global existence and uniqueness of strong solutions for initial data…

Analysis of PDEs · Mathematics 2013-04-23 Walter Craig , Xiangdi Huang , Yun Wang

We study a nonlocal variant of a thermodynamically consistent phase field model for binary mixtures of micropolar fluids, i.e., fluids exhibiting internal rotations. The model is described by a Navier--Stokes--Cahn--Hilliard system that…

Analysis of PDEs · Mathematics 2025-12-15 Kin Shing Chan , Kei Fong Lam

In this paper we consider a multiscale phase-field model for capillarity-driven flows in porous media. The presented model constitutes a reduction of the conventional Navier-Stokes-Cahn-Hilliard phase-field model, valid in situations where…

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 show short-time well-posedness of a diffuse interface model describing the flow of a fluid through a deformable porous medium consisting of two phases. The system non-linearly couples Biot's equations for poroelasticity, including…

Analysis of PDEs · Mathematics 2026-05-01 Helmut Abels , Jonas Haselböck

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

We are concerned with an initial boundary value problem for the nonhomogeneous heat conducting Navier-Stokes flows with non-negative density. First of all, we show that for the initial density allowing vacuum, the strong solution exists…

Analysis of PDEs · Mathematics 2017-08-08 Xin Zhong

We study dynamics of a coupled system consisting of the 3D Navier--Stokes equations which is linearized near a certain Poiseuille type flow in an (unbounded) domain and a classical (possibly nonlinear) elastic plate equation for transversal…

Analysis of PDEs · Mathematics 2012-12-12 Igor Chueshov , Iryna Ryzhkova

Accurately modeling the dynamics of high-density ratio ($\mathcal{O}(10^5)$) two-phase flows is important for many material science and manufacturing applications. This work considers numerical simulations of molten metal oscillations in…

Fluid Dynamics · Physics 2025-01-03 Ali Rabeh , Makrand A. Khanwale , John J. Lee , Baskar Ganapathysubramanian

The formal sharp-interface asymptotics in a degenerate Cahn-Hilliard model for viscoelastic phase separation with cross-diffusive coupling to a bulk stress variable are shown to lead to non-local lower-order counterparts of the classical…

Analysis of PDEs · Mathematics 2026-05-22 Katharina Hopf , John King , Andreas Münch , Barbara Wagner

In this paper, we are concerned with the global wellposedness of 2-D density-dependent incompressible Navier-Stokes equations with variable viscosity, in a critical functional frame- work which is invariant by the scaling of the equations…

Analysis of PDEs · Mathematics 2012-12-18 Jingchi Huang , Marius Paicu , Ping Zhang

We present an adaptive simulation framework for binary-fluid flows, based on the Abels-Garcke-Gr\"un Navier-Stokes-Cahn-Hilliard (AGG NSCH) diffuse-interface model. The adaptive-refinement procedure is guided by a two-level hierarchical…

Numerical Analysis · Mathematics 2022-09-28 T. H. B. Demont , G. J. van Zwieten , C. Diddens , E. H. van Brummelen

We analyze the pressureless Navier-Stokes system with nonlocal attraction-repulsion forces. Such systems appear in the context of models of collective behavior. We prove the existence of weak solutions on the whole space $\mathbb{R}^3$ in…

Analysis of PDEs · Mathematics 2024-02-19 Piotr B. Mucha , Maja Szlenk , Ewelina Zatorska

We are concerned with a model describing the motion of two compressible, immiscible fluids with density-dependent viscosity in the whole $\mathbb R^3$. The phases of the flow may have different pressure and viscosity laws and are separated…

Analysis of PDEs · Mathematics 2025-10-14 Marcel Zodji

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

This paper studies two well-known models for two-phase fluid flow at constant temperature, the isothermal Navier-Stokes-Allen-Cahn and the isothermal Navier-Stokes-Cahn-Hilliard equations, both of which consist of equations for the (total)…

Analysis of PDEs · Mathematics 2013-11-04 Heinrich Freistuhler , Matthias Kotschote

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

This paper is concerned with the large time behavior of the Cauchy problem for Navier-Stokes/Allen-Cahn system describing the interface motion of immiscible two-phase flow in 3-D. The existence and uniqueness of global solutions and the…

Analysis of PDEs · Mathematics 2021-10-28 Yazhou Chen , Hakho Hong , Xiaoding Shi