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This paper resolves the global regularity problem for the three-dimensional compressible magnetohydrodynamics (MHD) equations in the three-dimensional whole space, in the presence of a background magnetic field. Motivated by geophysical…

Analysis of PDEs · Mathematics 2026-05-13 Jincheng Gao , Xianpeng Hu , Lianyun Peng , Jiahong Wu

In this paper, we are concerned with the compressible viscous magnetohydrodynamic (MHD) system and investigate the large time behavior of strong solutions near constant equilibrium. In the eighties, Umeda, Kawashima and Shizuta initiated…

Analysis of PDEs · Mathematics 2017-10-03 Weixuan Shi , Jiang Xu

This paper is dedicated to the study of viscous compressible barotropic fluids in dimension N=2. We address the question of the global existence of strong solutions with large initial data for compressible Navier-Stokes system and Korteweg…

Analysis of PDEs · Mathematics 2012-11-21 Boris Haspot

We prove the global well-posedness for the 3-D micropolar fluid system in the critical Besov spaces by making a suitable transformation to the solutions and using the Fourier localization method, especially combined with a new $L^p$…

Analysis of PDEs · Mathematics 2011-12-20 Qionglei Chen , Changxing Miao

In this paper we prove the existence of solutions to the viscous, non-resistive magnetohydrodynamics (MHD) equations on the whole of $\mathbb{R}^{n}$, $n=2,3$, for divergence-free initial data in certain Besov spaces, namely…

Analysis of PDEs · Mathematics 2015-03-06 Jean-Yves Chemin , David S. McCormick , James C. Robinson , Jose L. Rodrigo

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 considers the initial boundary problem to the planar compressible magnetohydrodynamic equations with large initial data and vacuum. The global existence and uniqueness of large strong solutions are established when the heat…

Analysis of PDEs · Mathematics 2017-04-06 Jishan Fan , Shuxiang Huang , Fucai Li

In this paper, we investigate the global existence of strong solutions for the inhomogeneous incompressible viscoelastic system with only velocity dissipation on $\mathbb{R}^{2}$. Due to the criticality of the time-weight, the methods for…

Analysis of PDEs · Mathematics 2026-03-03 Chengfei Ai , Yong Wang , Yunshun Wu

Given solenoidal vector $u_0\in H^{-2\d}\cap H^1(\R^2),$ $\r_0-1\in L^2(\R^2),$ and $\r_0 \in L^\infty\cap\dot{W}^{1,r}(\R^2)$ with a positive lower bound for $\d\in (0,\f12)$ and $2<r<\f{2}{1-2\d},$ we prove that 2-D incompressible…

Analysis of PDEs · Mathematics 2013-01-14 Hammadi Abidi , Ping Zhang

In this paper, we consider the global wellposedness of 3-D incompressible magneto-hydrodynamical system with small and smooth initial data. The main difficulty of the proof lies in establishing the global in time $L^1$ estimate for the…

Analysis of PDEs · Mathematics 2013-05-14 Li Xu , Ping Zhang

We study the incompressible limit of the compressible non-isentropic ideal magnetohydrodynamic equations with general initial data in the whole space $\mathbb{R}^d$ ($d=2,3$). We first establish the existence of classic solutions on a time…

Analysis of PDEs · Mathematics 2016-03-08 Song Jiang , Qiangchang Ju , Fucai Li

The existence of global-in-time classical solutions to the Cauchy problem of incompressible Magnetohydrodynamic flows with zero magnetic diffusivity is considered in two dimensions. The linearization of equations is a degenerated…

Analysis of PDEs · Mathematics 2014-05-02 Xianpeng Hu , Fanghua Lin

We consider the Cauchy problem to the 3D barotropic compressible Navier-Stokes equation. We prove global well-posedness, assuming that the initial data $(\rho_0-1,u_0)$ has small norms in the critical Besov space…

Analysis of PDEs · Mathematics 2025-09-23 Zihua Guo , Zihao Song , Minghua Yang

We investigate the incompressible inhomogeneous magnetohydrodynamic equations in $\mathbb{R}^3$, under the assumptions that the initial density $\rho_0$ is only bounded, and the initial velocity $u_0$ and magnetic field $B_0$ exhibit…

Analysis of PDEs · Mathematics 2025-01-14 Fucai Li , Jinkai Ni , Ling-Yun Shou

We study the local existence of solutions to the magnetohydrodynamics (MHD) system describing the motion of a compressible, viscous, electrically and heat conducting fluid in the $L^p-L^q$ class with inhomogeneous boundary conditions. The…

Analysis of PDEs · Mathematics 2025-07-29 Mostafa Meliani

The Cauchy problem for the three-dimensional compressible flow of nematic liquid crystals is considered. Existence and uniqueness of the global strong solution are established in critical Besov spaces provided that the initial datum is…

Analysis of PDEs · Mathematics 2024-08-21 Xianpeng Hu , Hao Wu

In this paper, we consider the compressible Navier--Stokes system around the constant equilibrium states and prove the unique existence of a global solution for arbitrarily large initial data in the scaling critical Besov space provided…

Analysis of PDEs · Mathematics 2023-04-11 Mikihiro Fujii

In this paper, we are concerned with the global wellposedness of 2-D density-dependent incompressible Navier-Stokes equations with variable viscosity, in a critical functional frame- work which is invariant by the scaling of the equations…

Analysis of PDEs · Mathematics 2012-12-18 Jingchi Huang , Marius Paicu , Ping Zhang

This paper is concerned with the stability and large-time behavior for 3D magneto-micropolar equations with horizontal dissipation. The global well-posedness of the aforementioned system is established, with the initial data and its…

Analysis of PDEs · Mathematics 2025-09-25 Peng Lu , Yuanyuan Qiao

In this paper, we study the Cauchy's problem of the compressible Euler system with damping and establish the global-in-time well-posedness in $L^p$-type critical Besov spaces for $1\leq p<2$. To achieve it, a new product estimate is…

Analysis of PDEs · Mathematics 2026-02-27 Jianzhong Zhang , Ying Sui , Xiliang Li