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
View PDF on arXiv
48 Citations
Highly Influential Citations
2
Background Citations
16
Methods Citations
7
Results Citations
3

48 Citations

Determining wavenumbers for the incompressible Hall-magneto-hydrodynamics.

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…

Global smooth solutions of the 3D Hall-magnetohydrodynamic equations with large data.

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…

Dissipation wavenumber and regularity for electron magnetohydrodynamics

. 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…

Conservation and anomalous dissipation of physical quantities for the 3D electron-MHD

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…

A class of global large, smooth solutions for the magnetohydrodynamics with Hall and ion‐slip effects

  • 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…

A free boundary problem for planar compressible Hall-magnetohydrodynamic equations

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…

A free boundary problem for planar compressible Hall-magnetohydrodynamic equations

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…

A ug 2 01 9 DETERMINING WAVENUMBERS FOR THE INCOMPRESSIBLE HALL-MAGNETOHYDRODYNAMICS

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…

Local Well-Posedness and Blow-Up for the Solutions to the Axisymmetric Inviscid Hall-MHD Equations

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…

Derivation of the Hall-MHD Equations from the Navier–Stokes–Maxwell Equations

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…

References

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Well-posedness for Hall-magnetohydrodynamics