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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

In this paper, we prove the global existence of strong solutions to the two-dimensional compressible MHD equations with density dependent viscosity coefficients (known as Kazhikhov-Vaigant model) on 2D solid balls with arbitrary large…

Analysis of PDEs · Mathematics 2023-10-18 Xiangdi Huang , Wei Yan

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

In this note, we show the existence of regular solutions to the stationary version of the Navier-Stokes system for compressible fluids with a density dependent viscosity, known as the shallow water equations. For arbitrary large forcing we…

Analysis of PDEs · Mathematics 2016-07-15 Šimon Axmann , Piotr B. Mucha , Milan Pokorný

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 consider a compressible Navier-Stokes system for a barotropic fluid with density dependent viscosity in a three-dimensional time-space domain $(0,T)\times \Omega_\varepsilon$ where $\Omega_\varepsilon = (0,\varepsilon)^2\times (0,1)$. We…

Analysis of PDEs · Mathematics 2020-08-25 Matteo Caggio , Vaclav Macha

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 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

We study the barotropic compressible Navier-Stokes system where the shear viscosity is a positive constant and the bulk one proportional to a power of the density with the power bigger than one and a third. The system is subject to the…

Analysis of PDEs · Mathematics 2022-06-01 Xinyu Fan , Jiaxu Li , Jing Li

For smooth initial data, we establish the global existence and uniqueness of strong and classical solutions to the Cauchy problem for the barotropic compressible Navier-Stokes equations in two spatial dimensions with vacuum state as far…

Analysis of PDEs · Mathematics 2013-06-21 Xiangdi Huang , Jing Li

This paper is concerned with the large time behavior of the Cauchy problem for Navier-Stokes/Allen-Cahn system describing the interface motion of immiscible two-phase flow in 3-D. The existence and uniqueness of global solutions and the…

Analysis of PDEs · Mathematics 2021-10-28 Yazhou Chen , Hakho Hong , Xiaoding Shi

We consider a generalized alpha-type model in the whole three-dimensional space and driven by a stationary (time-independent) external force. This model contains as particular cases some relevant equations of the fluid dynamics, among them…

Analysis of PDEs · Mathematics 2024-01-02 Oscar Jarrin

We establish global well-posedness of strong solutions for the nonhomogeneous magnetohydrodynamic equations with density-dependent viscosity and initial density allowing vanish in two-dimensional (2D) bounded domains. Applying delicate…

Analysis of PDEs · Mathematics 2024-06-19 Xin Zhong

For periodic initial data with the density allowing vacuum, we establish the global existence and exponential decay of weak, strong and classical solutions to the two-dimensional(2D) compressible Navier-Stokes equations when the bulk…

Analysis of PDEs · Mathematics 2025-07-03 Qinghao Lei , Chengfeng Xiong

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 this short paper we establish the global well-posedness of strong solutions to the 3D full compressible Navier-Stokes system with vacuum in a bounded domain $\Omega\subset \mathbb{R}^3$ by the bootstrap argument provided that the…

Analysis of PDEs · Mathematics 2017-09-14 Jishan Fan , Fucai Li

In this paper, the one-dimensional compressible Navier-Stokes system with outer pressure boundary conditions is investigated. Under some suitable assumptions, we prove that the specific volume and the temperature are bounded from below and…

Analysis of PDEs · Mathematics 2022-06-01 Guocai Cai , Canpei Chen , Yanfang Peng

In this paper, we consider the radially symmetric compressible Navier-Stokes equations with swirl in two-dimensional disks, where the shear viscosity coefficient \(\mu = \text{const}> 0\), and the bulk one \(\lambda = \rho^\beta(\beta>0)\).…

Analysis of PDEs · Mathematics 2025-06-23 Xiangdi Huang , Weili Meng

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

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