# Regularity criterion for the 3D Hall-magneto-hydrodynamics

@article{Dai2015RegularityCF,
title={Regularity criterion for the 3D Hall-magneto-hydrodynamics},
author={Mimi Dai},
journal={arXiv: Analysis of PDEs},
year={2015}
}
• Mimi Dai
• Published 21 July 2015
• Physics
• arXiv: Analysis of PDEs
Using Littlewood-Paley theory, one formulates the determining wavenumbers for the Hall-MHD system, defined for each individual solution $(u,b)$. It is shown that the long time behaviour of strong
• Mathematics
• 2019
In this paper, we establish the global existence to the three-dimensional incompressible Hall-MHD equations for a class of large initial data, whose $L^{\infty}$ norms can be arbitrarily large. In
• Physics
• 2022
. We consider the electron magnetohydrodynamics (MHD) with static background ion ﬂow. A special situation of B ( x,y,t ) = ∇ × ( a~e z ) + b~e z with scalar-valued functions a ( x,y,t ) and b ( x,y,t
• Physics, Mathematics
• 2019
We study the three dimensional electron magnetohydrodynamics in a particular plasma context where the velocity of ion flow vanishes. We construct weak solutions with finite energy that do not
• Huali Zhang
• Mathematics
Mathematical Methods in the Applied Sciences
• 2022
In this paper, the Cauchy problem of fractional magnetohydrodynamic (MHD) system with the Hall and ion‐slip effects is considered. By exploring the structure of semilinear and quasilinear terms, we
• Mathematics
Zeitschrift für angewandte Mathematik und Physik
• 2018
In this paper, we study the existence and uniqueness of the global classical solution for the planar compressible Hall-magnetohydrodynamic equations with large initial data. The system is
• Mathematics
• 2018
In this paper, we study the existence and uniqueness of the global classical solution for the planar compressible Hall-magnetohydrodynamic equations with large initial data. The system is
The above system describes the evolution of a system consisting of a magnetic field b, electrons and ions, whose collective motion under b can be approximated as an electrically conducting fluid with
• Mathematics
• 2018
In this paper, we consider the regularity problem of the solutions to the axisymmetric, inviscid, and incompressible Hall-magnetohydrodynamics (Hall-MHD) equations. First, we obtain the local-in-time
• Physics
Journal of Nonlinear Science
• 2022
By using a set of scaling limits, the authors in Acheritogaray et al. (Kinet Relat Models 4:901–918, 2011) and Srinivasan and Shumlak (Phys Plasmas 18(9):620, 2011) proposed a framework of deriving

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