English
Related papers

Related papers: Global classical solution to 3D isentropic compres…

200 papers

This paper is concerned with the three-dimensional equations of a simplified hydrodynamic flow modeling the motion of compressible, nematic liquid crystal materials. The authors establish the global existence of classical solution to the…

Analysis of PDEs · Mathematics 2012-04-24 Jing Li , Zhonghai Xu , Jianwen Zhang

In this paper, we consider the three-dimensional isentropic Navier-Stokes equations for compressible fluids with viscosities depending on density in a power law and allowing initial vacuum. We introduce the notion of regular solutions and…

Analysis of PDEs · Mathematics 2015-04-14 Yachun Li , Ronghua Pan , Shengguo Zhu

In this paper, the Cauchy problem for the three-dimensional (3-D) full compressible Navier-Stokes equations (CNS) with zero thermal conductivity is considered. First, when shear and bulk viscosity coefficients both depend on the absolute…

Analysis of PDEs · Mathematics 2023-01-18 Qin Duan , Zhouping Xin , Shengguo Zhu

We consider the local well-posedness of strong and classical solutions to the three-dimensional barotropic compressible Navier-Stokes equations with density containing vacuum initially. We first prove the local existence and uniqueness of…

Analysis of PDEs · Mathematics 2019-05-29 Xiangdi Huang

We study an initial-boundary value problem of three-dimensional (3D) compressible isentropic magneto-micropolar fluid equations with Coulomb force and slip boundary conditions in a bounded simply connected domain, whose boundary has a…

Analysis of PDEs · Mathematics 2024-08-22 Yang Liu , Xin Zhong

The present paper aims at the investigation of the global stability of large solutions to the compressible Navier-Stokes equations in the whole space. Our main results and innovations can be concluded as follows: Under the assumption that…

Analysis of PDEs · Mathematics 2017-10-31 Lingbing He , Jingchi Huang , Chao Wang

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

The formation of singularity and breakdown of strong solutions to the two-dimensional (2D) Cauchy problem of the full compressible Navier-Stokes equations with zero heat conduction are considered. It is shown that for the initial density…

Analysis of PDEs · Mathematics 2017-06-08 Xin Zhong

In this paper, the three-dimensional (3D) isentropic compressible Navier-Stokes equations with degenerate viscosities (\textbf{ICND}) is considered in both the whole space and the periodic domain. First, for the corresponding Cauchy…

Analysis of PDEs · Mathematics 2019-11-20 Shengguo Zhu

We investigate the global stability of large solutions to the compressible isentropic Navier-Stokes equations in a three-dimensional (3D) bounded domain with Navier-slip boundary conditions. It is shown that the strong solutions converge to…

Analysis of PDEs · Mathematics 2025-10-17 Yang Liu , Guochun Wu , Xin Zhong

In this paper, we consider the initial-boundary value problems of the compressible isentropic Navier-Stokes equations with density-dependent viscosity on two dimensional solid balls which was first introduced by Kazhikhov where shear…

Analysis of PDEs · Mathematics 2023-10-10 Xiangdi Huang , Mengluan Su , Wei Yan , Rongfeng Yu

We consider the initial-boundary value problem (IBVP) for the isentropic compressible Navier-Stokes equations (\textbf{CNS}) in the domain exterior to a ball in $\mathbb R^d$ $(d=2\ \text{or} \ 3)$. When viscosity coefficients are given as…

Analysis of PDEs · Mathematics 2022-08-01 Yue Cao , Hao Li , 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

This paper investigates the global dynamics of a three-dimensional fluid-particle interaction system that couples the compressible barotropic Navier-Stokes equations with the Vlasov-Fokker-Planck equation through a density-dependent…

Analysis of PDEs · Mathematics 2026-03-10 Fucai Li , Jinkai Ni , Dehua Wang

We study global well-posedness of strong solutions for the nonhomogeneous Navier-Stokes equations with density-dependent viscosity and initial density allowing vanish in $\mathbb{R}^2$. Applying a logarithmic interpolation inequality and…

Analysis of PDEs · Mathematics 2021-03-01 Xin Zhong

We show that the classical Cauchy problem for the incompressible 3d Navier-Stokes equations with $(-1)$-homogeneous initial data has a global scale-invariant solution which is smooth for positive times. Our main technical tools are…

Analysis of PDEs · Mathematics 2012-04-04 Hao Jia , Vladimír Šverák

In this paper, we investigate the well-posedess of classical solutions to the Cauchy problem of Navier-Stokes equations,and prove that the classical solution with finite energy does not exist even in the inhomogeneous Sobolev space for any…

Analysis of PDEs · Mathematics 2018-11-21 Hailiang Li , Yuexun 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 this paper, we consider the global existence and uniqueness of the classical solutions for the 3D viscous liquid-gas two-phase flow model. Initial data is only small in the energy-norm. Our main ideas come from [15] where the existence…

Analysis of PDEs · Mathematics 2015-06-03 Haibo Cui , Huanyao Wen , Haiyan Yin

In this paper, we investigate the global existence of spherically symmetric strong solutions with large initial data to an initial-boundary value problem of the multidimensional isentropic compressible Navier-Stokes-Korteweg system in an…

Analysis of PDEs · Mathematics 2026-05-07 Zhengzheng Chen , Fanfan Jiang