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This paper is devoted to studying the Cauchy problem for the three-dimensional isentropic compressible Navier-Stokes equations with density-dependent viscosities given by $\mu=\rho^\alpha,\lambda=\rho^\alpha(\alpha>0)$. We establish the…

Analysis of PDEs · Mathematics 2025-07-23 Jie Fan , Xiangdi Huang , Anchun Ni

In this paper, we consider the global spherically symmetric strong solutions to the compressible Navier-Stokes equations with far-field vacuum and density-dependent degenerate viscosity, following the framework proposed by Bresch-Vasseur-Yu…

Analysis of PDEs · Mathematics 2026-05-05 Xingyang Zhang

We are concerned with the global existence and vanishing dispersion limit of strong/classical solutions to the Cauchy problem of the one-dimensional barotropic compressible quantum Navier-Stokes equations, which consists of the compressible…

Analysis of PDEs · Mathematics 2023-12-08 Zhengzheng Chen , Huijiang Zhao

This paper investigates the global existence of classical solutions to the isentropic compressible Navier-Stokes equations with slip boundary condition in a three-dimensional (3D) exterior domain. It is shown that the classical solutions…

Analysis of PDEs · Mathematics 2025-04-03 Minghong Xie , Saiguo Xu , Yinghui Zhang

We are concerned with the Cauchy problem of the two-dimensional (2D) nonhomogeneous incompressible Navier-Stokes equations with vacuum as far-field density. It is proved that if the initial density decays not too slow at infinity, the 2D…

Analysis of PDEs · Mathematics 2018-04-30 Boqiang Lv , Xiaoding Shi , Xin Zhong

In this paper, we consider the Cauchy problem for the three-dimensional barotropic compressible Navier-Stokes equations with density-dependent viscosities. By considering the system as an elliptic-dominated structure and defining suitable…

Analysis of PDEs · Mathematics 2024-08-09 Xiangdi Huang , Jiaxu Li , Rong Zhang

In this paper, we study the global well-posedness of classical solutions to the 2D compressible MHD equations with large initial data and vacuum. With the assumption $\mu=const.$ and $\lambda=\rho^\beta,~\beta>1$ (Va\v{i}gant-Kazhikhov…

Analysis of PDEs · Mathematics 2014-09-22 Yu Mei

First of all, we get the global existence of classical and strong solutions of the full compressible Navier-Stokes equations in three space dimensions with initial data which is large and spherically or cylindrically symmetric. The…

Analysis of PDEs · Mathematics 2012-04-19 Huanyao Wen , Changjiang Zhu

In this paper, we consider the three dimensional Cauchy problem of the compressible micropolar viscous flows, we prove the existence of unique global classical solution for smooth initial data with small initial energy but possibly large…

Analysis of PDEs · Mathematics 2022-12-28 Canze Zhu , Qiang Tao

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

For the initial boundary value problem of compressible barotropic Navier-Stokes equations in one-dimensional bounded domains with general density-dependent viscosity and large external force, we prove that there exists a unique global…

Analysis of PDEs · Mathematics 2018-08-10 Boqiang Lü , Yixuan Wang , Yuhang Wu

In this paper, we consider the 1D Navier-Stokes equations for viscous compressible and heat conducting fluids (i.e., the full Navier-Stokes equations). We get a unique global classical solution to the equations with large initial data and…

Analysis of PDEs · Mathematics 2011-03-09 Huanyao Wen , Changjiang Zhu

The full compressible Navier-Stokes system describing the motion of a viscous, compressible, heat-conductive, and Newtonian polytropic fluid is studied in a three-dimensional simply connected bounded domain with smooth boundary having a…

Analysis of PDEs · Mathematics 2022-07-04 Jing Li , Boqiang Lü , Xue Wang

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

We prove the global existence and uniqueness of the classical (weak) solution for the 2D or 3D compressible Navier-Stokes equations with a density-dependent viscosity coefficient ($\lambda=\lambda(\rho)$). Initial data and solutions are…

Analysis of PDEs · Mathematics 2009-04-13 Ting Zhang

We consider the Cauchy problem for one-dimensional (1D) barotropic compressible Navier-Stokes equations with density-dependent viscosity and large external force. Under a general assumption on the density-dependent viscosity, we prove that…

Analysis of PDEs · Mathematics 2018-08-24 Kexin Li , Boqiang Lü , Yixuan Wang

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 are concerned with the Cauchy problem for one-dimensional compressible isentropic Navier-Stokes equations with density-dependent viscosity $\mu(\rho)=\rho^\alpha (\alpha>0)$ and pressure $P(\rho)=\rho^{\gamma}\…

Analysis of PDEs · Mathematics 2015-06-04 Changsheng Dou , Quansen Jiu

In this paper, the Cauchy problem for the one-dimensional (1-D) isentropic compressible Navier-Stokes equations (\textbf{CNS}) is considered. When the viscosity $\mu(\rho)$ depends on the density $\rho$ in a sublinear power law ($…

Analysis of PDEs · Mathematics 2022-06-14 Yue Cao , Hao Li , Shengguo Zhu

We study the barotropic compressible Navier-Stokes equations with Navier-type boundary condition in a two-dimensional simply connected bounded domain with $C^{\infty}$ boundary $\partial\Omega.$ By some new estimates on the boundary related…

Analysis of PDEs · Mathematics 2021-04-22 Yuebo Cao