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This paper analytically investigates the Darcy-Poisson-Nernst-Planck system. This system is a mathematical model for electrolyte solutions. In this paper, we consider electrolyte solutions, which consist of a neutral fluid and multiple…

Analysis of PDEs · Mathematics 2016-05-25 Matthias Herz , Peter Knabner

This article is devoted to the derivation and analysis of a system of partial differential equations modeling a diffuse interface flow of two Newtonian incompressible magnetic fluids. The system consists of the incompressible Navier-Stokes…

Analysis of PDEs · Mathematics 2020-04-22 Martin Kalousek , Sourav Mitra , Anja Schlömerkemper

We continue our study on the global solution to the two-dimensional Prandtl's system for unsteady boundary layers in the class considered by Oleinik provided that the pressure is favorable. First, by using a different method from [13], we…

Analysis of PDEs · Mathematics 2022-05-04 Zhouping Xin , Liqun Zhang , Junning Zhao

In this paper, we study the well-posedeness at low regularity of a two-dimensional system obtained as a reduced model for micropolar fluid dynamics. At the mathematical level, the system presents a coupling between an Euler-type equation…

Analysis of PDEs · Mathematics 2026-05-14 Francesco Fanelli , Pedro Gabriel Fernández Dalgo

We consider a diffuse interface model for an incompressible isothermal mixture of two viscous Newtonian fluids with different densities in a bounded domain in two or three space dimensions. The model is the nonlocal version of the one…

Analysis of PDEs · Mathematics 2015-06-01 Sergio Frigeri

In this paper, we study the global well-posedness of a coupled system of kinetic and fluid equations. More precisely, we establish the global existence of weak solutions for Navier-Stokes-BGK system consisting of the BGK model of Boltzmann…

Analysis of PDEs · Mathematics 2018-01-26 Young-Pil Choi , Seok-Bae Yun

A compressible Oldroyd--B type model with stress diffusion is derived from a compressible Navier--Stokes--Fokker--Planck system arising in the kinetic theory of dilute polymeric fluids, where polymer chains immersed in a barotropic,…

Analysis of PDEs · Mathematics 2016-08-16 John W. Barrett , Yong Lu , Endre Süli

We prove global existence of weak solutions for a version of one velocity Baer-Nunziato system with dissipation describing a mixture of two non interacting viscous compressible fluids in a piecewise regular Lipschitz domain with general…

Analysis of PDEs · Mathematics 2021-05-12 Stanislav Kracmar , Young-Sam Kwon , Sarka Necasova , Antonin Novotny

In three space dimensions, we consider the compressible inviscid model describing the time evolution of two fluids sharing the same velocity and enjoying the algebraic pressure closure. By employing the technique of convex integration, we…

Analysis of PDEs · Mathematics 2019-12-24 Yang Li , Ewelina Zatorska

We study a thermodynamically consistent diffuse-interface model that describes the motion of two macroscopically immiscible, incompressible, and viscous Newtonian fluids with unmatched densities. This model is compatible with continuum…

Analysis of PDEs · Mathematics 2026-04-30 Mingwen Fei , Xiang Fei , Yadong Liu , Hao Wu

This article establishes the global existence of weak solutions to a model proposed by Rosensweig (Rosensweig, Ferrohydrodynamics (1985)) for the dynamics of ferrofluids. The system is expressed by the conservation of linear momentum, the…

Analysis of PDEs · Mathematics 2019-10-02 Ricardo H. Nochetto , Konstantina Trivisa , Franziska Weber

We consider weak solutions to a two-dimensional simplified Ericksen-Leslie system of compressible flow of nematic liquid crystals. An initial-boundary value problem is first studied in a bounded domain. By developing new techniques and…

Analysis of PDEs · Mathematics 2013-08-13 Fei Jiang , Song Jiang , Dehua Wang

We prove the global existence of weak solutions to the Navier-Stokes equations of compressible heat-conducting fluids in two spatial dimensions with initial data and external forces which are large and spherically symmetric. The solutions…

Analysis of PDEs · Mathematics 2012-05-01 Fei Jiang , Song Jiang , Junpin Yin

This paper deals with the derivation and analysis of the the Hall Magneto-Hydrodynamic equations. We first provide a derivation of this system from a two-fluids Euler-Maxwell system for electrons and ions, through a set of scaling limits.…

Mathematical Physics · Physics 2014-04-08 Marion Arichetogaray , Pierre Degond , Amic Frouvelle , Jian-Guo Liu

This paper concerns the global-in-time evolution of a generic compressible two-fluid model in $\mathbb{R}^d$ ($d\geq3$) with the common pressure law. Due to the non-dissipative properties for densities and two different particle paths…

Analysis of PDEs · Mathematics 2025-02-11 Ling-Yun Shou , Jiayan Wu , Lei Yao , Yinghui Zhang

We study the global existence of classical solutions for two-dimensional incompressible MHD system with only magnetic diffusion. By using the time-weighted lower-order energy and uniformly bounded higher-order energy estimates, we prove the…

Analysis of PDEs · Mathematics 2023-10-27 Yuanyuan Qiao

We study the anisotropic, incompressible Cahn-Hilliard-Navier-Stokes system with variable density in a bounded smooth domain $\Omega \subset \mathbb{R}^d$. This work extends previous results on the isotropic case by incorporating…

Analysis of PDEs · Mathematics 2026-03-30 Azeddine Zaidni , Saad Benjelloun , Radouan Boukharfane

Introducing a new notion of generalized suitable weak solutions, we first prove validity of the energy inequality for such a class of weak solutions to the Navier-Stokes equations in the whole space $\mathbb{R}^n$. Although we need certain…

Analysis of PDEs · Mathematics 2018-05-15 Hideo Kozono , Yutaka Terasawa , Yuta Wakasugi

In the first part of this paper, we prove the existence of global strong solution for Korteweg system in one dimension. In the second part, motivated by the processes of vanishing capillarity-viscosity limit in order to select the…

Analysis of PDEs · Mathematics 2011-10-25 Frédéric Charve , Boris Haspot

This paper concerns the existence of global weak solutions {\it \`a la Leray} for compressible Navier--Stokes--Fourier systems with periodic boundary conditions and the truncated virial pressure law which is assumed to be thermodynamically…

Analysis of PDEs · Mathematics 2023-05-15 Didier Bresch , Pierre-Emmanuel Jabin , Fei Wang