English
Related papers

Related papers: Compressible flows with a density-dependent viscos…

200 papers

In this paper, we extend considerably the global existence results of entropy-weak solutions related to compressible Navier-Stokes system with density dependent viscosities obtained, independently (using different strategies), by Vasseur-Yu…

Analysis of PDEs · Mathematics 2019-05-08 Didier Bresch , Alexis Vasseur , Cheng Yu

This paper is concerned with the Cauchy problem of Navier-Stokes equations for compressible viscous heat-conductive fluids with far-field vacuum at infinity in $\R^3$. For less regular data and weaker compatibility condition than those…

Analysis of PDEs · Mathematics 2021-10-28 Suhua Lai , Hao Xu , Jianwen Zhang

We prove that any weak space-time $L^2$ vanishing viscosity limit of a sequence of strong solutions of Navier-Stokes equations in a bounded domain of ${\mathbb{R}}^2$ satisfies the Euler equation if the solutions' local enstrophies are…

Analysis of PDEs · Mathematics 2017-12-06 Peter Constantin , Vlad Vicol

We consider the one-dimensional Cauchy problem for the Navier-Stokes equations with degenerate viscosity coefficient in highly compressible regime. It corresponds to the compressible Navier-Stokes system with large Mach number equal to…

Analysis of PDEs · Mathematics 2015-12-03 Boris Haspot , Ewelina Zatorska

In this paper, we study the vanishing viscosity of the isentropic compressible Navier-Stokes equations with density dependent viscous coefficient in the presence of the shock wave. Given a shock wave to the corresponding Euler equations, we…

Analysis of PDEs · Mathematics 2019-05-16 Meiying Cui

A fundamental open problem in the theory of the multidimensional compressible Navier-Stokes equations is whether smooth solutions can develop singularities in finite time. For constant viscosity coefficients, recent remarkable results show…

Analysis of PDEs · Mathematics 2026-03-25 Gui-Qiang G. Chen , Lihui Liu , Shengguo Zhu

Recently, for periodic initial data with initial density allowed to vanish, Huang and Li [1] establish the global existence of strong and weak solutions for the two-dimensional compressible Navier{Stokes equations with no restrictions on…

Analysis of PDEs · Mathematics 2012-06-21 Fei Jiang

In a three-dimensional bounded domain $\Omega$ we consider the compressible Navier-Stokes equations for a barotropic fluid with general non-linear density dependent viscosities and no-slip boundary conditions. A nonlinear drag term is added…

Analysis of PDEs · Mathematics 2025-02-11 Luca Bisconti , Matteo Caggio , Filippo Dell'Oro

This paper is a continuation of our previous work (arXiv:2507.03505), where the global existence and incompressible limit of weak solutions to the isentropic compressible Navier-Stokes equations in the half-plane with ripped density and…

Analysis of PDEs · Mathematics 2025-10-28 Shuai Wang , Guochun Wu , Xin Zhong

This paper is dedicated to the global existence of entropy weak solutions for the Poisson-Nernst-Planck-Compressible Navier-Stokes system in a periodic domain $\Pi$ d when the shear viscosity $\mu$($\rho$) = $\mu$ $\rho$ with $\mu$ to be…

Analysis of PDEs · Mathematics 2026-03-13 Didier Bresch , Maria Kazakova , Charlotte Tonnelier

We prove the existence of weak solutions to steady, compressible non-Newtonian Navier-Stokes system on a bounded, two- or three-dimensional domain. Assuming the viscous stress tensor is monotone satisfying a power-law growth with power $r$…

Analysis of PDEs · Mathematics 2024-01-11 Cosmin Burtea , Maja Szlenk

In this paper we are concerned with a non-isothermal compressible Navier-Stokes-Fourier model with density dependent viscosity that vanish on the vacuum. We prove the global existence of weak solutions with large data in the…

Analysis of PDEs · Mathematics 2017-12-08 Boling Guo , Binqiang Xie

In this paper, we investigate a system coupled by nonhomogeneous incompressible Navier-Stokes equations and Allen-Cahn equations describing a diffuse interface for two-phase flow of viscous fluids with different densities in a bounded…

Analysis of PDEs · Mathematics 2025-03-06 Yinghua Li , Wenlin Ye

In this paper, we study the global well-posedness of the 2D compressible Navier-Stokes equations with large initial data and vacuum. It is proved that if the shear viscosity $\mu$ is a positive constant and the bulk viscosity $\l$ is the…

Analysis of PDEs · Mathematics 2012-02-08 Quansen Jiu , Yi Wang , Zhouping Xin

In 1995, Kazhikhov and Vaigant introduced a particular class of isentropic compressible Navier-Stokes equations with variable viscosity coefficients and, for the first time, established the existence of global smooth solutions for…

Analysis of PDEs · Mathematics 2025-12-23 Jie Fan , Xiangdi Huang

In the recent paper, the global-in-time inviscid limit of the three-dimensional (3D) isentropic compressible Navier-Stokes equations is considered. First, when viscosity coefficients are given as a constant multiple of density's power…

Analysis of PDEs · Mathematics 2019-11-21 Yongcai Geng , Yachun Li , Shengguo Zhu

In this paper, we consider the Cauchy problem to the heat conductive compressible Navier-Stokes equations in the presence of vacuum and with vacuum far field. Global well-posedness of strong solutions is established under the assumption,…

Analysis of PDEs · Mathematics 2020-05-20 Jinkai Li

This paper studies the two-dimensional inhomogeneous Navier--Stokes equations governing stratified flows in a bounded domain under a gravitational potential \(f\). Our main results are as follows. First, we provide a rigorous…

Analysis of PDEs · Mathematics 2025-12-23 Song Jiang , Quan Wang

So far existence of dissipative weak solutions for the compressible Navier-Stokes equations (i.e. weak solutions satisfying the relative energy inequality) is known only in the case of boundary conditions with non zero inflow/outflow (i.e.,…

Analysis of PDEs · Mathematics 2019-05-08 Young-Sam Kwon , Antonin Novotny , Vladyslav Satko

In this paper, we are first interested in the compressible Navier-Stokes equations with densitydependent viscosities in bounded domains with on-homogeneous Dirichlet conditions. We study the wellposedness of such models with non-constant…

Analysis of PDEs · Mathematics 2009-06-09 Laurent Chupin , Rémy Sart