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In this paper, we investigate the global existence of weak solutions to 3-D inhomogeneous incompressible MHD equations with variable viscosity and resistivity, which is sufficiently close to $1$ in $L^\infty(\mathbb{R}^3),$ provided that…

Analysis of PDEs · Mathematics 2025-03-04 Hammadi Abidi , Guilong Gui , Ping Zhang

This paper concerns the study of the incompressible Euler equations with variable density, in the case of space dimension $d=2$. Contrarily to their homogeneous (constant density) counterpart, those equations are not known to be well-posed…

Analysis of PDEs · Mathematics 2025-02-17 Francesco Fanelli

In this paper, we consider the Cauchy problem to the planar magnetohydrodynamics (MHD) system with both constant viscosity and constant resistivity but without heat conductivity. Global well-posedness of strong solutions in the presence of…

Analysis of PDEs · Mathematics 2025-06-24 Jinkai Li , Mingjie Li

We study the Cauchy problem for the three-dimensional isentropic compressible ideal (inviscid and non-resistive) magnetohydrodynamic equations with velocity damping on the periodic torus $\mathbb{T}^3$. The system admits a steady…

Analysis of PDEs · Mathematics 2026-05-07 Liening Qiao , Jiahong Wu , Fuyi Xu , Xiaoping Zhai

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 incompressible limit of the compressible non-isentropic magnetohydrodynamic equations with zero magnetic diffusivity and general initial data in the whole space $\mathbb{R}^d$ $(d=2,3)$. We first establish the existence of…

Analysis of PDEs · Mathematics 2011-11-15 Song Jiang , Qiangchang Ju , Fucai Li

We obtain the global well-posedness to the 3D incompressible magnetohydrodynamics (MHD) equations in Besov space with negative index of regularity. Particularly, we can get the global solutions for a new class of large initial data. As a…

Analysis of PDEs · Mathematics 2015-09-28 Renhui Wan

In this paper, we prove that suitable weak solution $(u,b)$ of the 3-D MHD equations can be extended beyond $T$ if $u\in L^\infty(0,T;L^3(\R^3))$ and the horizontal components $b_h$ of the magnetic field satisfies the well-known…

Analysis of PDEs · Mathematics 2016-03-09 Wendong Wang

We consider the Cauchy problem of the non-isentropic compressible magnetohydrodynamic equations in $\mathbb{R}^3$ with far-field vacuum. By deriving delicate energy estimates and exploiting the intrinsic structure of the system, we…

Analysis of PDEs · Mathematics 2025-12-24 Lin Xu , Xin Zhong

In this paper, we consider the full compressible, viscous, non-resistive MHD system under the assumption that the fluids move on a plane while the magnetic field is oriented vertically. Within the framework of Besov spaces, by introducing…

Analysis of PDEs · Mathematics 2024-08-15 Xiaoping Zhai , Shunhang Zhang

We prove the local well-posedness of the 3D free-boundary incompressible ideal magnetohydrodynamics (MHD) equations with surface tension, which describe the motion of a perfect conducting fluid in an electromagnetic field. We adapt the…

Analysis of PDEs · Mathematics 2023-12-13 Xumin Gu , Chenyun Luo , Junyan Zhang

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 solves the global conormal regularity problem for the three-dimensional incompressible MHD equations with slip boundary condition near a background magnetic field. Motivated by applications in geophysics, the MHD system…

Analysis of PDEs · Mathematics 2025-07-01 Jincheng Gao , Jiahong Wu , Zheng-an Yao , Xuan Yin

The combustion model is studied in three-dimensional (3D) smooth bounded domains with various types of boundary conditions. The global existence and uniqueness of strong solutions are obtained under the smallness of the gradient of initial…

Analysis of PDEs · Mathematics 2023-10-17 Jiawen Zhang

This paper establishes the local-in-time existence and uniqueness of strong solutions in $H^{s}$ for $s > n/2$ to the viscous, non-resistive magnetohydrodynamics (MHD) equations in $\mathbb{R}^{n}$, $n=2, 3$, as well as for a related model…

Analysis of PDEs · Mathematics 2014-01-21 C. L. Fefferman , D. S. McCormick , J. C. Robinson , J. L. Rodrigo

This paper concerns with the explicit blowup phenomenon for 3D incompressible MHD equations in R^3. More precisely, we find two family of explicit blowup solutions for 3D incompressible MHD equations in R^3. One family of solutions admit…

Analysis of PDEs · Mathematics 2018-07-20 Weiping Yan

In this paper, we prove the global existence of smooth solutions to the three-dimensional incompressible magneto-hydrodynamical system with initial data close enough to the equilibrium state, $(e_3,0).$ Compared with the the previous works…

Analysis of PDEs · Mathematics 2015-11-11 Hammadi Abidi , Ping Zhang

In this article, we show that the magneto-hydrodynamic system (MHD) in $\R^N$ with variable density, variable viscosity and variable conductivity has a local weak solution in the Besov space $\dot B^{\frac{N}{p_1}}_{p_1,1}(\R^N)\times\dot…

Analysis of PDEs · Mathematics 2008-06-23 Hammadi Abidi , Marius Paicu

In this paper, we investigate the solvability, regularity and the vanishing dissipation limit of solutions to the three-dimensional viscous magneto-hydrodynamic (MHD) equations in bounded domains. On the boundary, the velocity field…

Analysis of PDEs · Mathematics 2020-07-07 Qin Duan , Yuelong Xiao , Zhouping Xin

The full compressible magnetohydrodynamic system in three-dimensional exterior domains is investigated. For the initial-boundary-value problem of this system with slip boundary condition for the velocity, adiabatic one for the temperature,…

Analysis of PDEs · Mathematics 2022-11-02 Yunkun Chen , Yi Peng , Xue Wang