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We consider Navier-Stokes equations for compressible viscous fluids in one dimension. We prove the existence of global strong solution with large initial data for the shallow water system. The key ingredient of the proof relies to a new…

Analysis of PDEs · Mathematics 2018-04-02 Boris Haspot

Motivated by \cite{CG10,CZ6}, we prove the global existence of solutions to the two-dimensional isentropic compressible Navier-Stokes equations with smooth initial data which are slowly varying in one direction and with initial density…

Analysis of PDEs · Mathematics 2021-06-04 Yong Lu , Ping Zhang

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 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 this paper, we study the Cauchy problem to the 3D fractional compressible isentropic generalized Navier-Stokes equations for viscous compressible fluid with one Levy diffusion process. We obtain the existence and uniqueness of global…

Analysis of PDEs · Mathematics 2024-07-03 Mengqian Liu , Lei Niu , Zhigang Wu

We establish the global-in-time existence of solutions of the Cauchy problem for the full Navier-Stokes equations for compressible heat-conducting flow in multidimensions with initial data that are large, discontinuous, spherically…

Analysis of PDEs · Mathematics 2022-08-11 Gui-Qiang G. Chen , Yucong Huang , Shengguo Zhu

In this paper, we investigate the global well-posedness and optimal time-decay of classical solutions for the 3-D full compressible Navier-Stokes system, which is given by the motion of the compressible viscous and heat-conductive gases.…

Analysis of PDEs · Mathematics 2025-03-20 Wenwen Huo , Chao Zhang

We prove global existence of solutions to the Cauchy problem for the compressible Navier-Stokes equations in Euclidean spaces, given initial data with small norms in Besov and critical weighted Besov spaces. Global existence and a priori…

Analysis of PDEs · Mathematics 2023-12-12 Dáithí Ó hAodha

This paper is concerned with the large-time behavior of solutions to the initial and initial boundary value problems with large initial data for the compressible Navier-Stokes system describing the one-dimensional motion of a viscous…

Analysis of PDEs · Mathematics 2024-06-11 Jing Li , Zhilei Liang

We consider the one-dimensional compressible Navier-Stokes system with constant viscosity and the nonlinear heat conductivity being proportional to a positive power of the temperature which may be degenerate. This problem is imposed on the…

Analysis of PDEs · Mathematics 2022-02-16 Guocai Cai , Yanfang Peng , Yi Peng

The compressible Navier-Stokes system with the constant viscosity and the nonlinear heat conductivity which is proportional to a positive power of the temperature and may be degenerate is considered. Under the outer pressure boundary…

Analysis of PDEs · Mathematics 2025-04-16 Manyu Liu , Yanfang Peng , Zhilun Peng

In this paper, we establish global strong solutions for arbitrarily large initial data to the 2D and 3D compressible Navier-Stokes-Korteweg system, also referred to as the quantum Navier-Stokes equations, originally derived by Dunn and…

Analysis of PDEs · Mathematics 2026-02-12 Xiangdi Huang , Yongteng Gu , Muxi Lei

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 prove the global well-posedness of the classical solution to the 2D Cauchy problem of the compressible Navier-Stokes equations with arbitrarily large initial data when the shear viscosity $\mu$ is a positive constant and…

Analysis of PDEs · Mathematics 2012-09-04 Quansen Jiu , Yi Wang , Zhouping Xin

In this paper, we construct a family of global-in-time solutions of the 3-D full compressible Navier-Stokes (N-S) equations with temperature-dependent transport coefficients (including viscosity and heat-conductivity), and show that at…

Analysis of PDEs · Mathematics 2024-02-26 Meichen Hou , Lingjun Liu , Shu Wang , Lingda Xu

In this paper, we study the three-dimensional axisymmetric compressible Navier-Stokes equations with slip boundary conditions in a cylindrical domain excluding the axis. We establish the global existence and exponential decay of weak,…

Analysis of PDEs · Mathematics 2025-11-19 Qinghao Lei

We present a new hydrodynamic model consisting of the pressureless Euler equations and the isentropic compressible Navier-Stokes equations where the coupling of two systems is through the drag force. This coupled system can be derived, in…

Analysis of PDEs · Mathematics 2016-04-19 Young-Pil Choi , Bongsuk Kwon

For the equations of a planar magnetohydrodynamic (MHD) compressible flow with the viscosity depending on the specific volume of the gas and the heat conductivity being proportional to a positive power of the temperature, we obtain global…

Analysis of PDEs · Mathematics 2024-06-19 Yuebo Cao , Yi Peng , Ying Sun

We investigate the three dimensional compressible Navier-Stokes and the continuity equations in Cartesian coordinates for Newtonian fluids. The polytropic equation of sate is used as closing condition. The key idea is the three-dimensional…

Fluid Dynamics · Physics 2014-07-08 I. F. Barna

This paper investigates the Cauchy problem of two-dimensional full compressible Navier-Stokes system with density and temperature vanishing at infinity. For the strong solutions, some a priori weighted $L^2(R^2)$-norm of the gradient of…

Analysis of PDEs · Mathematics 2023-04-05 Xue Wang