Well-posedness for Hall-magnetohydrodynamics

D Chae, P Degond, JG Liu - Annales de l'IHP Analyse non linéaire, 2014 - numdam.org
We prove local existence of smooth solutions for large data and global smooth solutions for
small data to the incompressible, resistive, viscous or inviscid Hall-MHD model. We also …

Kinetic formulation and global existence for the Hall-Magneto-hydrodynamics system

M Arichetogaray, P Degond, A Frouvelle… - arXiv preprint arXiv …, 2011 - arxiv.org
This paper deals with the derivation and analysis of the the Hall Magneto-Hydrodynamic
equations. We first provide a derivation of this system from a two-fluids Euler-Maxwell …

[HTML][HTML] On the blow-up criterion and small data global existence for the Hall-magnetohydrodynamics

D Chae, J Lee - Journal of Differential Equations, 2014 - Elsevier
In this paper, we establish an optimal blow-up criterion for classical solutions to the
incompressible resistive Hall-magnetohydrodynamic equations. We also prove two global-in …

Local well-posedness for the Hall-MHD equations with fractional magnetic diffusion

D Chae, R Wan, J Wu - Journal of Mathematical Fluid Mechanics, 2015 - Springer
Abstract The Hall-magnetohydrodynamics (Hall-MHD) equations, rigorously derived from
kinetic models, are useful in describing many physical phenomena in geophysics and …

[HTML][HTML] Singularity formation for the incompressible Hall-MHD equations without resistivity

D Chae, S Weng - Annales de l'Institut Henri Poincaré C, Analyse non …, 2016 - Elsevier
In this paper we show that the incompressible Hall-MHD system without resistivity is not
globally in time well-posed in any Sobolev space H m (R 3) for any m> 7 2. Namely, either …

[HTML][HTML] Space–time decay estimates for the incompressible viscous resistive MHD and Hall-MHD equations

S Weng - Journal of Functional Analysis, 2016 - Elsevier
In this paper, we address the space–time decay properties for strong solutions to the
incompressible viscous resistive Hall-MHD equations. We obtained the same space–time …

Global well-posedness for the 3D incompressible Hall-magnetohydrodynamic equations with Fujita–Kato type initial data

R Wan, Y Zhou - Journal of Mathematical Fluid Mechanics, 2019 - Springer
Abstract Hall-magnetohydrodynamic (Hall-MHD) equations which can be derived from two
fluids model or kinetic models [see Acheritogaray et al.(Kinet Relat Models 4: 901–918 …

On the weak solutions to the Maxwell–Landau–Lifshitz equations and to the Hall–Magneto–Hydrodynamic equations

E Dumas, F Sueur - Communications in Mathematical Physics, 2014 - Springer
In this paper we deal with weak solutions to the Maxwell–Landau–Lifshitz equations and to
the Hall–Magneto–Hydrodynamic equations. First we prove that these solutions satisfy some …

Wellposedness of the electron MHD without resistivity for large perturbations of the uniform magnetic field

IJ Jeong, SJ Oh - arXiv preprint arXiv:2402.06278, 2024 - arxiv.org
We prove the local wellposedness of the Cauchy problems for the electron
magnetohydrodynamics equations (E-MHD) without resistivity for possibly large …

[HTML][HTML] On analyticity and temporal decay rates of solutions to the viscous resistive Hall-MHD system

S Weng - Journal of Differential Equations, 2016 - Elsevier
We address the analyticity and large time decay rates for strong solutions of the Hall-MHD
equations. By Gevrey estimates, we show that the strong solution with small initial date in H r …