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Related papers: Global weak solutions to a diffuse-interface model…

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We consider a two-phase problem for two incompressible, viscous and immiscible fluids which are separated by a sharp interface. The problem arises as a sharp interface limit of a diffuse interface model. We present results on local…

Analysis of PDEs · Mathematics 2012-09-17 Helmut Abels , Mathias Wilke

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

This paper concerns the global well-posedness and large time asymptotic behavior of strong and classical solutions to the Cauchy problem of the Navier-Stokes equations for viscous compressible barotropic flows in two or three spatial…

Analysis of PDEs · Mathematics 2021-02-22 Jing Li , Zhouping Xin

In this paper, we investigate the wellposedness of the non-isentropic compressible Navier-Stokes/Allen-Cahn system with the heat-conductivity proportional to a positive power of the temperature. This system describes the flow of a two-phase…

Analysis of PDEs · Mathematics 2020-11-13 Yazhou Chen , Qiaolin He , Bin Huang , Xiaoding Shi

In this work we study a degenerate pseudo-parabolic system with cross diffusion describing the evolution of the densities of an unsaturated two-phase flow mixture with dynamic capillary pressure in porous medium with saturation-dependent…

Analysis of PDEs · Mathematics 2019-05-27 Esther S. Daus , Josipa-Pina Milišić , Nicola Zamponi

We study a one dimensional model for two-phase flows in heterogeneous media, in which the capillary pressure functions can be discontinuous with respect to space. We first give a model, leading to a system of degenerated non-linear…

Analysis of PDEs · Mathematics 2009-09-08 Clément Cancès

We analyze a quasi-incompressible Cahn--Hilliard--Navier--Stokes system (qCHNS) for two-phase flows with unmatched densities. The order parameter is the volume fraction difference of the two fluids, while mass-averaged velocity is adopted.…

Analysis of PDEs · Mathematics 2026-04-28 Mingwen Fei , Xiang Fei , Daozhi Han , Yadong Liu

In this paper, we first prove the global existence of weak solutions to the d-dimensional incompressible inhomogeneous Navier-Stokes equations with initial data in critical Besov spaces, which satisfies a non-linear smallness condition. The…

Analysis of PDEs · Mathematics 2015-06-12 Jingchi Huang , Marius Paicu , Ping Zhang

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

We consider a two-dimensional MHD model describing the evolution of viscous, compressible and electrically conducting fluids under the action of vertical magnetic field without resistivity. Existence of global weak solutions is established…

Analysis of PDEs · Mathematics 2019-07-02 Yang Li , Yongzhong Sun

We introduce a simple model of the time evolution of a binary mixture of compressible fluids including the thermal effects. Despite its apparent simplicity, the model is thermodynamically consistent admitting an entropy balance equation. We…

Analysis of PDEs · Mathematics 2021-09-07 Eduard Feireisl , Madalina Petcu , Bangwei She

We establish the global existence of a class of weak solutions to the isentropic compressible Navier-Stokes and magnetohydrodynamic (MHD) equations on the whole plane under a suitably small initial energy. The solutions constructed here…

Analysis of PDEs · Mathematics 2026-02-09 Shuai Wang , Xin Zhong

This paper investigates the Cauchy problem for the barotropic compressible Navier-Stokes equations in $\mathbb{R}^2$ with the constant state as far field, which may be vacuum or non-vacuum. Under the assumption of a sufficiently large bulk…

Analysis of PDEs · Mathematics 2026-01-27 Qinghao Lei , Chengfeng Xiong

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

In this paper we study the well-posedness and long-time dynamics of a diffuse-interface model for the mixture of two viscous incompressible Newtonian fluids with thermo-induced Marangoni effects. The governing system consists of modified…

Analysis of PDEs · Mathematics 2013-02-26 Hao Wu , Xiang Xu

In [1], the Authors rigorously establish the relaxation limit from the Quantum Navier Stokes Poisson (QNSP) system to the Quantum Drift Diffusion (QDD) equation, while providing only a brief outline of the global existence theory for weak…

Analysis of PDEs · Mathematics 2025-12-10 Giada Cianfarani Carnevale

In this paper, we consider the global well-posedness of the initial-boundary value problem to a nonlinear Boussinesq-fluid-structure interaction system, which describes the motion of an incompressible Boussinesq-fluid surrounded by an…

Analysis of PDEs · Mathematics 2025-02-14 J. Zhang , S. Wang , L. Shen

The paper is concerned with the mathematical analysis of a class of thermodynamically consistent kinetic models for nonisothermal flows of dilute polymeric fluids, based on the identification of energy storage mechanisms and entropy…

Analysis of PDEs · Mathematics 2026-04-10 Miroslav Bulíček , Josef Málek , Endre Süli

In many occurrences of fluid-structure interaction time-periodic motions are observed. We consider the interaction between a fluid driven by the three dimensional Navier-Stokes equation and a two dimensional linearized elastic Koiter shell…

Analysis of PDEs · Mathematics 2024-01-31 Claudiu Mîndrilă , Sebastian Schwarzacher

The global-in-time existence of weak solutions to a degenerate Cahn-Hilliard cross-diffusion system with singular potential in a bounded domain with no-flux boundary conditions is proved. The model consists of two coupled parabolic…

Analysis of PDEs · Mathematics 2024-01-11 Ansgar Jüngel , Yue Li