## 48 Citations

### Determining wavenumbers for the incompressible Hall-magneto-hydrodynamics.

- Physics
- 2019

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.

- 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…

### Dissipation wavenumber and regularity for electron magnetohydrodynamics

- 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…

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

- 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…

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

- MathematicsMathematical 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

- MathematicsZeitschrift 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…

### A free boundary problem for planar compressible Hall-magnetohydrodynamic equations

- 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…

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

- Physics
- 2019

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

- MathematicsAdvances in Mathematical Physics
- 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…

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

- PhysicsJournal 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…

## References

SHOWING 1-10 OF 21 REFERENCES

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

- Physics, Mathematics
- 2011

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 system for electrons and…

### On the blow-up criterion and small data global existence for the Hall-magnetohydrodynamics

- Mathematics
- 2013

### Regularity Criterion and Energy Conservation for the Supercritical Quasi-geostrophic Equation

- Mathematics, Environmental Science
- 2015

This paper studies the regularity and energy conservation problems for the 2D supercritical quasi-geostrophic (SQG) equation. We apply an approach of splitting the dissipation wavenumber to obtain a…

### Quantitative Analytical Model for Magnetic Reconnection in Hall Magnetohydrodynamics

- Physics
- 2009

Magnetic reconnection is of fundamental importance for laboratory and naturally occurring plasmas. Reconnection usually develops on time scales which are much shorter than those associated with…

### Quantitative, comprehensive, analytical model for magnetic reconnection in Hall magnetohydrodynamics.

- PhysicsPhysical review letters
- 2008

The theory describes a two-dimensional reconnection diffusion region, provides expressions for reconnection rates, and derives a formal criterion for fast reconnection in terms of dissipation parameters and d{i}.

### Studies on Magneto-Hydrodynamic Waves and other Anisotropic wave motions

- GeologyPhilosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences
- 1960

There are two separate but closely interwoven strands of argument in this paper; one mainly mathematical, and one mainly physical. The mathematical strand begins with a method of asymptotically…

### A Unified Approach to Regularity Problems for the 3D Navier-Stokes and Euler Equations: the Use of Kolmogorov’s Dissipation Range

- Mathematics
- 2011

Motivated by Kolmogorov’s theory of turbulence we present a unified approach to the regularity problems for the 3D Navier-Stokes and Euler equations. We introduce a dissipation wavenumber…

### A Maximum Principle Applied to Quasi-Geostrophic Equations

- Mathematics
- 2004

We study the initial value problem for dissipative 2D Quasi-geostrophic equations proving local existence, global results for small initial data in the super-critical case, decay of Lp-norms and…