A POINTWISE BOUND ON THE ELECTROMAGNETIC FIELD GENERATED BY A COLLISIONLESS PLASMA

2005 ◽  
Vol 15 (09) ◽  
pp. 1371-1391 ◽  
Author(s):  
CHRISTOPHE PALLARD
Keyword(s):  
Electromagnetic Field ◽  
Collisionless Plasma ◽  
System Of Equations ◽  
Maxwell System ◽  
Smooth Solutions ◽  
Pointwise Bound

The behaviour of a collisionless plasma is described by the relativistic Vlasov–Maxwell system of equations. A criteria ensuring the existence of smooth solutions was given8by Glassey and Strauss, along with pointwise bounds on the electromagnetic field generated by the particles. In this paper, we obtain an improved bound.

scholarly journals ANALYTICAL MODELS FOR QUARK STARS

2007 ◽  
Vol 16 (11) ◽  
pp. 1803-1811 ◽  
Author(s):  
K. KOMATHIRAJ ◽  
S. D. MAHARAJ
Keyword(s):  
Electromagnetic Field ◽  
Equation Of State ◽  
Exact Solutions ◽  
Quark Matter ◽  
Matter Content ◽  
Analytical Models ◽  
System Of Equations ◽  
Maxwell System ◽  
Elementary Functions ◽  
Quark Stars

We find two new classes of exact solutions to the Einstein–Maxwell system of equations. The matter content satisfies a linear equation of state consistent with quark matter; a particular form of one of the gravitational potentials is specified to generate solutions. The exact solutions can be written in terms of elementary functions, and these can be related to quark matter in the presence of an electromagnetic field. The first class of solutions generalizes the Mak–Harko model. The second class of solutions does not admit any singularities in the matter and gravitational potentials at the center.

scholarly journals Convergence of a Singular Euler-Maxwell Approximation of the Incompressible Euler Equations

2011 ◽  
Vol 2011 ◽  
pp. 1-13
Author(s):  
Jianwei Yang ◽  
Hongli Wang
Keyword(s):  
Euler Equations ◽  
Collisionless Plasma ◽  
Maxwell System ◽  
Energy Estimation ◽  
Incompressible Euler Equations ◽  
Incompressible Euler

This paper studies the Euler-Maxwell system which is a model of a collisionless plasma. By energy estimation and the curl-div decomposition of the gradient, we rigorously justify a singular approximation of the incompressible Euler equations via a quasi-neutral regime.

Regularity of weak solutions for the relativistic Vlasov–Maxwell system

2018 ◽  
Vol 15 (04) ◽  
pp. 693-719 ◽  
Author(s):  
Nicolas Besse ◽  
Philippe Bechouche
Keyword(s):  
Electromagnetic Field ◽  
Weak Solutions ◽  
Existence And Uniqueness ◽  
Regularity Of Solutions ◽  
Maxwell System ◽  
Smoothing Effect ◽  
Regular Solutions ◽  
Low Velocity ◽  
Regularity Of Weak Solutions ◽  
The One

We investigate the regularity of weak solutions of the relativistic Vlasov–Maxwell system by using Fourier analysis and the smoothing effect of low velocity particles. This smoothing effect has been used by several authors (see Glassey and Strauss 1986; Klainerman and Staffilani, 2002) for proving existence and uniqueness of [Formula: see text]-regular solutions of the Vlasov–Maxwell system. This smoothing mechanism has also been used to study the regularity of solutions for a kinetic transport equation coupled with a wave equation (see Bouchut, Golse and Pallard 2004). Under the same assumptions as in the paper “Nonresonant smoothing for coupled wave[Formula: see text]+[Formula: see text]transport equations and the Vlasov–Maxwell system”, Rev. Mat. Iberoamericana 20 (2004) 865–892, by Bouchut, Golse and Pallard, we prove a slightly better regularity for the electromagnetic field than the one showed in the latter paper. Namely, we prove that the electromagnetic field belongs to [Formula: see text], with [Formula: see text].

PARAXIAL APPROXIMATION OF THE VLASOV-MAXWELL SYSTEM: LAMINAR BEAMS

1994 ◽  
Vol 04 (02) ◽  
pp. 203-221 ◽  
Author(s):  
A. NOURI
Keyword(s):  
Electromagnetic Field ◽  
Charged Particle ◽  
Initial Data ◽  
Global Existence ◽  
Local Existence ◽  
Sufficient Conditions ◽  
External Electromagnetic Field ◽  
Evolution System ◽  
Lagrangian Coordinates ◽  
Maxwell System

The Vlasov-Maxwell stationary system for charged particle laminar beams is studied with a paraxial model of approximation. It leads to a degenerate evolution system, which local existence is proved. Then, using lagrangian coordinates, with sufficient conditions on the initial data and the external electromagnetic field, it is shown that global existence is possible.

scholarly journals A SLOWLY ROTATING CHARGED BLACK HOLE IN FIVE DIMENSIONS

2006 ◽  
Vol 21 (09) ◽  
pp. 751-757 ◽  
Author(s):  
A. N. ALIEV
Keyword(s):  
General Relativity ◽  
Black Hole ◽  
System Of Equations ◽  
Maxwell System ◽  
Five Dimensions ◽  
Four Dimensions ◽  
Higher Dimensional ◽  
Long Time ◽  
Electrically Charged ◽  
Black Hole Solutions

Black hole solutions in higher dimensional Einstein and Einstein–Maxwell gravity have been discussed by Tangherlini as well as Myers and Perry a long time ago. These solutions are the generalizations of the familiar Schwarzschild, Reissner–Nordström and Kerr solutions of four-dimensional general relativity. However, higher dimensional generalization of the Kerr–Newman solution in four dimensions has not been found yet. As a first step in this direction we shall report on a new solution of the Einstein–Maxwell system of equations that describes an electrically charged and slowly rotating black hole in five dimensions.

scholarly journals The Dual Continuity Equations

2018 ◽  
Author(s):  
Arbab Arbab ◽  
Norah N. Alsaawi
Keyword(s):  
Electromagnetic Field ◽  
Wave Equation ◽  
Gauge Invariance ◽  
Maxwell Equations ◽  
Continuity Equation ◽  
Mathematical Structure ◽  
Magnetic Monopoles ◽  
System Of Equations ◽  
Duality Transformation ◽  
Continuity Equations

The ordinary continuity equation relating the current and density of a system is extended to incorporate systems with dual (longitudinal and transverse) currents. Such a system of equations is found to have the same mathematical structure as that of Maxwell equations. The horizontal and transverse currents and the densities associated with them are found to be coupled to each other. Each of these quantities are found to obey a wave equation traveling at the velocity of light in vacuum. London's equations of super-conductivity are shown to emerge from some sort of continuity equations. The new London's equations are symmetric and are shown to be dual to each other. It is shown that London's equations are Maxwell's equations with massive electromagnetic field (photon). These equations preserve the gauge invariance that is broken in other massive electrodynamics. The duality invariance may allow magnetic monopoles to be present inside superconductors. The new duality is called the comprehensive duality transformation.

scholarly journals Optimal control of the two-dimensional Vlasov-Maxwell system

2020 ◽  
Author(s):  
Jörg Weber
Keyword(s):  
Adjoint Equation ◽  
Collisionless Plasma ◽  
Three Dimensional ◽  
Classical Solutions ◽  
Two Dimensional ◽  
Maxwell System ◽  
Global Classical Solutions ◽  
Global Existence Of Solutions ◽  
Dimensional Version ◽  
The One

The time evolution of a collisionless plasma is modeled by the Vlasov-Maxwell system which couples the Vlasov equation (the transport equation) with the Maxwell equations of electrodynamics. We only consider a two-dimensional version of the problem since existence of global, classical solutions of the full three-dimensional problem is not known. We add external currents to the system, in applications generated by coils, to control the plasma properly. After considering global existence of solutions to this system, differentiability of the control-to-state operator is proved. In applications, on the one hand, we want the shape of the plasma to be close to some desired shape. On the other hand, a cost term penalizing the external currents shall be as small as possible. These two aims lead to minimizing some objective function. We restrict ourselves to only such control currents that are realizable in applications. After that, we prove existence of a minimizer and deduce first order optimality conditions and the adjoint equation.

A convergence to the Navier–Stokes–Maxwell system with solenoidal Ohm's law from a two-fluid model

2020 ◽  
pp. 1-22
Author(s):  
Zeng Zhang
Keyword(s):  
Electromagnetic Field ◽  
Transfer Coefficient ◽  
Fluid Model ◽  
Navier Stokes ◽  
Maxwell System ◽  
Ohm’S Law ◽  
Momentum Transfer Coefficient ◽  
Ohm's Law ◽  
Two Fluid Model ◽  
Two Fluid

We show the incompressible Navier–Stokes–Maxwell system with solenoidal Ohm's law can be derived from the two-fluid incompressible Navier–Stokes–Maxwell system when the momentum transfer coefficient tends to zero. The strategy is based on the decay and dissipative properties of the electromagnetic field.

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