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We study a diffuse-interface model that describes the dynamics of two-phase incompressible flows driven by the thermo-induced Marangoni effect. The hydrodynamic system consists of the Navier-Stokes equations for the fluid velocity, the…

Analysis of PDEs · Mathematics 2026-05-26 Lingxi Chen , Hao Wu

The Navier-Stokes systems for compressible fluids with density-dependent viscosities are considered in the present paper. These equations, in particular, include the ones which are rigorously derived recently as the Saint-Venant system for…

Analysis of PDEs · Mathematics 2008-11-26 Hai-Liang Li , Jing Li , Zhouping Xin

The equations of stationary compressible flows of active liquid crystals are considered in a bounded three-dimensional domain. The system consists of the stationary Navier-Stokes equations coupled with the equation of Q-tensors and the…

Analysis of PDEs · Mathematics 2022-05-03 Zhilei Liang , Apala Majumdar , Dehua Wang , Yixuan Wang

In this paper, we revisit the joint low-Mach and low-Frode number limit for the compressible Navier-Stokes equations with degenerate, density-dependent viscosity. Employing the relative entropy framework based on the concept of…

Analysis of PDEs · Mathematics 2025-12-01 Nilasis Chaudhuri , Francesco Fanelli , Yang Li , Ewelina Zatorska

We prove the global existence of weak solutions for the 2-D compressible Navier-Stokes equations with a density-dependent viscosity coefficient ($\lambda=\lambda(\rho)$). Initial data and solutions are small in energy-norm with nonnegative…

Analysis of PDEs · Mathematics 2009-02-13 Ting Zhang , Daoyuan Fang

In this paper, we introduce a model describing the dynamic of vesicle membranes within an incompressible viscous fluid in $3D$ domains. The system consists of the Navier-Stokes equations, with an extra stress tensor depending on the…

Analysis of PDEs · Mathematics 2017-10-10 Blanca Climent-Ezquerra , Francisco Guillén-González

In this paper, we consider a two-dimensional non-resistive magnetohydrodynamic model, taking the fluctuation of absolute temperature into account. Combining the method of weak convergence developed by Lions [20], Feireisl et al. [7, 8] from…

Analysis of PDEs · Mathematics 2020-09-15 Yang Li , Yongzhong Sun

We study a Navier-Stokes/Cahn-Hilliard system modeling the evolution of a compressible binary mixture of viscous fluids undergoing phase separation. The novelty of this work is a free energy potential including the physically relevant…

Analysis of PDEs · Mathematics 2025-06-10 Danica Basarić , Andrea Giorgini

We study the global strong solutions to the compressible Navier-Stokes system with potential temperature transport in $\mathbb{R}^n.$ Different from the Navier-Stokes-Fourier system, the pressure is a nonlinear function of the density and…

Analysis of PDEs · Mathematics 2023-04-04 Xiaoping Zhai , Yongsheng Li , Fujun Zhou

We study the Navier-Stokes system describing the motion of a compressible viscous fluid driven by a nonlinear multiplicative stochastic force. We establish local in time existence (up to a positive stopping time) of a unique solution, which…

Analysis of PDEs · Mathematics 2016-06-20 Dominic Breit , Eduard Feireisl , Martina Hofmanova

We prove weak-strong uniqueness results for the compressible Navier-Stokes system with degenerate viscosity coefficient and with vacuum in one dimension. In other words, we give conditions on the weak solution constructed in \cite{Jiu} so…

Analysis of PDEs · Mathematics 2014-12-01 Boris Haspot

In the spirit of D. Hoff's weak solution theory for the compressible Navier-Stokes equations (CNS) with bounded density, in this paper we establish the global existence and regularity properties of finite-energy weak solutions to an initial…

Analysis of PDEs · Mathematics 2025-09-03 Jin Tan , Yan-Lin Wang , Lan Zhang

We consider a Navier-Stokes model for compressible fluids in one space dimension. We show that it can be approximated by a time-discrete scheme combining the discretization of a trivial stochastic differential equation and the application…

Analysis of PDEs · Mathematics 2012-11-09 Yann Brenier

This paper is dedicated to the study of viscous compressible barotropic fluids in dimension N=2. We address the question of the global existence of strong solutions with large initial data for compressible Navier-Stokes system and Korteweg…

Analysis of PDEs · Mathematics 2012-11-21 Boris Haspot

We consider the compressible Navier-Stokes equation with density dependent viscosity coefficients, focusing on the case where those coefficients vanish on vacuum. We prove the stability of weak solutions both in the torus and in the whole…

Analysis of PDEs · Mathematics 2007-05-23 Antoine Mellet , Alexis F. Vasseur

We prove the global existence and uniqueness of strong solutions for a compressible multifluid described by the barotropic Navier-Stokes equations in dim = 1. The result holds when the diffusion coefficient depends on the pressure. It…

Mathematical Physics · Physics 2010-12-30 C. Michoski , A. Vasseur

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

In this paper, we investigate the incompressible Navier-Stokes equations coupled with the Vlasov-Fokker-Planck equation, which describes a two-phase mixture of the viscous incompressible fluid with particles or bubbles through a frictional…

Analysis of PDEs · Mathematics 2026-02-04 Renjun Duan , Fengqiang Shi , Wendong Wang , Jianbo Yu

We are concerned with the barotropic compressible Navier-Stokes equations on the real line. Our primary goal is to establish the global well-posedness in a critical regularity framework in the case where the initial data are small…

Analysis of PDEs · Mathematics 2026-03-17 Raphaël Danchin

The global-in-time existence of weak solutions to the barotropic compressible quantum Navier-Stokes equations with damping is proved for large data in three dimensional space. The model consists of the compressible Navier-Stokes equations…

Analysis of PDEs · Mathematics 2015-08-26 Alexis F. Vasseur , Cheng Yu