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Here we prove the existence of global in time regular solutions to the two-dimensional compressible Navier-Stokes equations supplemented with arbitrary large initial velocity $v\_0$ and almost constantdensity $\varrho\_0$, for large volume…

Analysis of PDEs · Mathematics 2016-03-24 Raphaël Danchin , Piotr B. Mucha

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

We study the global well-posedness of magnetohydrodynamic (MHD) equations. The hydrodynamic system consists of the Navier-Stokes equations for the fluid velocity coupled with a reduced from of the Maxwell equations for the magnetic field.…

Analysis of PDEs · Mathematics 2019-08-09 Chengfei Ai , Zhong Tan , Jianfeng Zhou

By observing a new relation between the magnetic pressure and the hydrodynamic pressure, global existence of classical solution to the full perfect MHD equations with large data is established, in particular including the case when all the…

Analysis of PDEs · Mathematics 2013-12-03 Xulong Qin , Tong Yang , Zheng-an Yao , Wenshu Zhou

We address the compressible magnetohydrodynamics (MHD) equations in $\mathbb{R}^3$ and establish a blow-up criterion for the local strong solutions in terms of the density only. Namely, if the density is away from vacuum ($\rho= 0$) and the…

Analysis of PDEs · Mathematics 2020-12-08 Anthony Suen

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 first show local-in-time well-posedness of the compressible Navier-Stokes equations, assuming striated regularity while no other smoothness or smallness conditions on the initial density. With these local-in-time solutions served as…

Analysis of PDEs · Mathematics 2024-05-21 Xian Liao , Sagbo Marcel Zodji

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 prove the global well-posedness of three dimensional compressible Navier-Stokes equations for some classes of large initial data, which is of large oscillation for the density and large energy for the velocity. The structure of the…

Analysis of PDEs · Mathematics 2011-11-15 Chao Wang , Wei Wang , Zhifei Zhang

In this article we study the global regularity of 2D generalized magnetohydrodynamic equations (2D GMHD), in which the dissipation terms are $- \nu (- \triangle)^{\alpha} u$ and $- \kappa (-\triangle)^{\beta} b$. We show that smooth…

Analysis of PDEs · Mathematics 2013-02-28 Chuong V. Tran , Xinwei Yu , Zhichun Zhai

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

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

This paper investigates the non-resistive compressible magnetohydrodynamic (MHD) equations in $\mathbb{R}^2$. We establish the global existence and stability of classical solutions for initial data sufficiently close to a constant…

Analysis of PDEs · Mathematics 2026-05-22 Yi Zhu

This paper is concerned with an initial and boundary value problem of the one-dimensional planar MHD equations for viscous, heat-conducting, compressible, ideal polytropic fluids with constant transport coefficients and large data. The…

Analysis of PDEs · Mathematics 2020-02-19 Xia Ye , Jianwen Zhang

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

We study the large bulk viscosity limit for the compressible magnetohydrodynamics (MHD) equations in two and three dimensions. For arbitrarily large initial data in critical Besov spaces, we prove the global well-posedness of strong…

Analysis of PDEs · Mathematics 2026-02-06 Gennaro Ciampa , Donatella Donatelli , Giada Pellecchia

This paper concerns the Cauchy problem of two-dimensional (2D) full compressible magnetohydrodynamic (MHD) equations in the whole plane $\mathbb{R}^2$ with zero density at infinity. By spatial weighted energy method, we derive the local…

Analysis of PDEs · Mathematics 2022-05-18 Hong Chen , Xin Zhong

This paper is concerned with the Cauchy problem for the modified two-dimensional (2D) nonhomogeneous incompressible Navier-Stokes equations with density-dependent viscosity. By fully using the structure of the system, we can obtain the key…

Analysis of PDEs · Mathematics 2026-02-02 Bing Yuan , Rong Zhang , Peng Zhou

Due to the absence of dissipation mechanism to the inviscid compressible systems, it is a challenging problem to prove their global solvability. In this paper, we are concerned with the initial-boundary value problem to the inviscid and…

Analysis of PDEs · Mathematics 2025-08-20 Jinkai Li , Liening Qiao

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

This paper concerns the Dirichlet problem of three-dimensional inhomogeneous Navier-Stokes equations with density-dependent viscosity. When the viscosity coefficient $\mu(\rho)$ is a power function of the density ($\mu(\rho)=\mu\rho^\alpha$…

Analysis of PDEs · Mathematics 2024-08-02 Xiangdi Huang , Jiaxu Li , Rong Zhang