Nonunique Weak Solutions in Leray--Hopf Class for the Three-Dimensional Hall-MHD System

M Dai - SIAM journal on mathematical analysis, 2021 - SIAM
Nonunique weak solutions in Leray--Hopf class are constructed for the three-dimensional
magneto-hydrodynamics with Hall effect. We adapt the widely appreciated convex …

Local well-posedness for the Hall-MHD system in optimal Sobolev spaces

M Dai - Journal of differential equations, 2021 - Elsevier
We show that the viscous resistive magnetohydrodynamics system with Hall effect is locally
well-posed in H s (R 3)× H s+ 1− ε (R 3) with s> 1 2 and any small enough ε> 0 such that s …

[HTML][HTML] Long time behavior of solutions to the 3D Hall-magneto-hydrodynamics system with one diffusion

M Dai, H Liu - Journal of Differential Equations, 2019 - Elsevier
This paper studies the asymptotic behavior of smooth solutions to the generalized Hall-
magneto-hydrodynamics system (1.1) with one single diffusion on the whole space R 3. We …

[HTML][HTML] A class large solution of the 3D Hall-magnetohydrodynamic equations

J Li, Y Yu, W Zhu - Journal of Differential Equations, 2020 - Elsevier
A class large solution of the 3D Hall-magnetohydrodynamic equations - ScienceDirect Skip
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On the continuation principle of local smooth solution for the Hall-MHD equations

RP Agarwal, AMA Alghamdi, S Gala… - Applicable …, 2022 - Taylor & Francis
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Beale–Kato–Majda regularity criterion of smooth solutions for the Hall-MHD equations with zero viscosity

S Gala, E Galakhov, MA Ragusa, O Salieva - Bulletin of the Brazilian …, 2021 - Springer
In this paper, we investigate the Cauchy problem for the 3D incompressible Hall-MHD
equations with zero viscosity. We prove the Beale–Kato–Majda regularity criterion of smooth …

Global existence of 2D electron MHD near a steady state

M Dai - arxiv preprint arxiv:2306.13036, 2023 - arxiv.org
We study the electron magnetohydrodynamics (MHD) in two dimensional geometry, which
has a rich family of steady states. In an anisotropic resistivity context, we show global in time …

On uniqueness and helicity conservation of weak solutions to the electron-MHD system

M Dai, J Krol, H Liu - Journal of Mathematical Fluid Mechanics, 2022 - Springer
On Uniqueness and Helicity Conservation of Weak Solutions to the Electron-MHD System |
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Dissipation wavenumber and regularity for electron magnetohydrodynamics

M Dai, C Wu - Journal of Differential Equations, 2023 - Elsevier
We consider the electron magnetohydrodynamics (MHD) with static background ion flow. A
special situation of B (x, y, t)=∇×(ae→ z)+ be→ z with scalar-valued functions a (x, y, t) and b …

[HTML][HTML] Global existence and exponential stability of solutions for planar compressible Hall-magnetohydrodynamic equations

Q Tao, Y Yang, Z Yao - Journal of Differential Equations, 2017 - Elsevier
An initial-boundary value problem for Hall-magnetohydrodynamics in one space dimension
with general large initial data is investigated. We establish uniform pointwise positive lower …