English
Related papers

Related papers: Non-uniform decay of MHD equations with and withou…

200 papers

We analyze the decay laws of the kinetic and magnetic energies and the evolution of correlation lengths in freely decaying incompressible magnetohydrodynamic (MHD) turbulence. Scale invariance of MHD equations assures that, in the case of…

Astrophysics · Physics 2009-11-10 Leonardo Campanelli

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

We study the two-dimensional generalized magnetohydrodynamics system with generalized dissipation and diffusion in terms of fractional Laplacians. It is known that the classical magnetohydrodynamics system with full Laplacians in both…

Analysis of PDEs · Mathematics 2013-09-23 Kazuo Yamazaki

In this paper, we obtain the global well-posedness and the asymptotic behavior of solution of non-resistive 2D MHD problem on the half space. We overcome the difficulty of zero spectrum gap by building the relationship between half space…

Analysis of PDEs · Mathematics 2024-01-22 Jiakun Jin , Yoshiyuki Kagei , Xiaoxia Ren , Lei Wang , Cuili Zhai

This paper examines the uniqueness of weak solutions to the d-dimensional magnetohydrodynamic (MHD) equations with the fractional dissipation $(-\Delta)^\alpha u$ and without the magnetic diffusion. Important progress has been made on the…

Analysis of PDEs · Mathematics 2019-04-15 Quansen Jiu , Xiaoxiao Suo , Jiahong Wu , Huan Yu

This paper is concerned with the incompressible limit of the compressible magnetohydrodynamic equations with vanishing viscosity coefficients and general initial data in the whole space $\mathbb{R}^d$ $ (d=2$ or 3). It is rigorously showed…

Analysis of PDEs · Mathematics 2015-05-13 Song Jiang , Qiangchang Ju , Fucai Li

This paper concerns the Cauchy problem of the nonhomogeneous incompressible magnetohydrodynamic (MHD) equations on the whole two-dimensional (2D) space with vacuum as far field density. In particular, the initial density can have compact…

Analysis of PDEs · Mathematics 2015-06-17 Boqiang Lv , Zhonghai Xu , Xin Zhong

We investigate the effect of numerical magnetic diffusion in magnetohydrodynamic simulations of magnetically supported molecular clouds. To this end, we have performed numerical studies on adaptive mesh isothermal simulations of marginally…

Astrophysics of Galaxies · Physics 2022-01-26 Guido Granda-Muñoz , Enrique Vázquez-Semadeni , Gilberto C. Gómez , Manuel Zamora-Avilés

The authors study the Cauchy problem of the magnetohydrodynamic equations for viscous compressible barotropic flows in two or three spatial dimensions with vacuum as far field density. For two spatial dimensions, we establish the global…

Analysis of PDEs · Mathematics 2014-05-21 Boqiang Lv , Xiaoding Shi , Xinying Xu

At the zero temperature limit, a one-dimensional steady solution to the hydrodynamic equation of a U(2) invariant superfluid is obtained. This solution reveals that the magnitude of magnetization is always directly proportional to the…

Quantum Gases · Physics 2025-04-03 Guang-Xin Pang , Yi-Cai Zhang

In this article, we study the stability and large time behavior for an multi-dimensional incompressible magnetohydrodynamical system with a velocity damping term, for small perturbations near a steady-state of magnetic field fulfilling the…

Analysis of PDEs · Mathematics 2025-12-30 Hui Fang , Pingping Gui , Yanping Zhou

In this paper, we deal with the $2\frac{1}{2}$ dimensional Hall MHD by taking the velocity field $u$ and the magnetic field $B$ of the form $u(t,x,y)=\left(\nabla^{\perp}\phi(t,x,y), W(t,x,y)\right)$ and…

Analysis of PDEs · Mathematics 2021-11-03 Hantaek Bae , Kyungkeun Kang

Single fluid magnetohydrodynamic (MHD) equations have been studied through direct numerical simulations (DNS) using pseudo-spectral methods in two as well as three spatial dimensions. At Alfv\'en resonance, a reversible periodic exchange of…

Plasma Physics · Physics 2019-06-24 Rupak Mukherjee , Rajaraman Ganesh , Abhijit Sen

We consider the Cauchy problem to the three-dimensional isentropic compressible Magnetohydrodynamics (MHD) system with density-dependent viscosities. When the initial density is linearly equivalent to a large constant state, we prove that…

Analysis of PDEs · Mathematics 2024-08-20 Yachun Li , Peng Lu , Zhaoyang Shang

We study the effects of homogenous and isotropic initial conditions on decaying Magnetohydrodynamics (MHD). We show that for an initial distribution of velocity and magnetic field fluctuations, appropriately defined structure functions…

chao-dyn · Physics 2009-10-31 Abhik Basu

In recent years, the global existence of classical solutions to the Cauchy problem for 2D incompressible viscous MHD equations without magnetic diffusion has been proved in \cite{Ren,TZhang}, under the assumption that initial data is close…

Analysis of PDEs · Mathematics 2025-05-22 Shijin Ding , Ronghua Pan , Yi Zhu

This paper is concerned with existence of solutions to the incompressible non-resistive viscous magnetohydrodynamic (MHD) equations with large initial perturbations in there-dimensional (3D) periodic domains (in Lagrangian coordinates).…

Analysis of PDEs · Mathematics 2021-11-19 Fei Jiang , Song Jiang

In this paper, two classes of exact analytic time-dependent soultion of magnetic annihilation for incompressible magnetic fluid, have been obtained by solving the magnetohydrodynamic (MHD) equations directly. The solutions derived here…

Plasma Physics · Physics 2007-05-23 Xue-Shang Feng , Yong Liu , Feng-Si Wei , Zhan-Yin Ye

In this note we consider the ideal compressible magneto-hydrodynamics (MHD) equations in a special two dimensional setting. We show that there exist particular initial data for which one obtains infinitely many entropy-conserving weak…

Analysis of PDEs · Mathematics 2021-02-04 Christian Klingenberg , Simon Markfelder

In this paper, we prove a blow-up criterion in terms of the magnetic field $H$ and the mass density $\rho$ for the strong solutions to the $3$D compressible isentropic MHD equations with zero magnetic diffusion and initial vacuum. More…

Analysis of PDEs · Mathematics 2018-06-14 Shuai Xi , Shengguo Zhu