Related papers: Regularized derivatives in a 2-dimensional model o…
The main objective of this Report is to formulate the general theoretical framework of electromagnetic scattering by discrete random media rooted in the Maxwell-Lorentz electromagnetics and discuss its immediate analytical and numerical…
We consider the $3$-dimensional relativistic Vlasov-Maxwell system with data without compact support in momentum space. We prove two continuation criteria for solutions to this system. First, we show that a regular solution can be continued…
We outline a regular way for solving Maxwell's equations. We take, as the starting point, the notion of vector potentials. The rationale for introducing this notion in electrodynamics is that the set of Maxwell's equations is seemingly…
We present a simple model of interaction of the Maxwell equations with a matter field defined by the Klein-Gordon equation. A simple linear interaction and a nonlinear perurbation produce solutions of the equations containing hylomorphic…
Recently, an increasing interest in astrophysical as well as laboratory plasmas has been manifested in reference to the existence of relativistic flows, related in turn to the production of intense electric fields in magnetized systems.…
Stationary circularly symmetric solutions of General Relativity with negative cosmological constant coupled to the Maxwell field are analyzed in three spacetime dimensions. Taking into account that the fall-off of the fields is slower than…
The Magneto-Hydrodynamic (MHD) system of equations governs viscous fluids subject to a magnetic field and is derived via a coupling of the Navier-Stokes equations and Maxwell's equations. Recently it has become common to study…
Maxwell's equation, Dirac's equation and the equation of gravito-electromagnetism are shown to be particular instances of the extended Maxwell system. The equations are discussed in the framework of the theory of evolutionary equations.…
In the first sections of this article, we discuss two variations on Maxwell's equations that have been introduced in earlier work--a class of nonlinear Maxwell theories with well-defined Galilean limits (and correspondingly generalized…
A method to derive stationary solutions of the relativistic Vlasov-Maxwell system is explored. In the non-relativistic case, a method using the Hermite polynomial series to describe the deviation from the Maxwell-Boltzmann distribution is…
We prove the existence of a $L^2$-normalized solitary wave solution for the Maxwell-Dirac equations in (3+1)-Minkowski space. In addition, for the Coulomb-Dirac model, describing fermions with attractive Coulomb interactions in the…
The inadequacy of Li\'{e}nard-Wiechert potentials is demonstrated as one of the examples related to the inconsistency of the conventional classical electrodynamics. The insufficiency of the Faraday-Maxwell concept to describe the whole…
Dimensional regularization of Euclidean momentum space integrals is a highly successful technique in renormalization of quantum field theories. While it yields a straightforward algorithmic method, with which to evaluate diagrams beyond…
We consider the 2D Maxwell--Lorentz system which describes a rotating particle coupled to the Maxwell field. The system admits stationary soliton-type solutions. We prove the attraction to solitons for any finite energy solution relying on…
We investigate the three-dimensional compressible Euler-Maxwell system, a model for simulating the transport of electrons interacting with propagating electromagnetic waves in semiconductor devices. First, we show the global well-posedness…
We show the existence and uniqueness of a DiPerna-Lions flow for relativistic particles subject to a Lorentz force in an electromagnetic field. The electric and magnetic fields solves the linear Maxwell system in the void but for singular…
Certain power-counting non-renormalizable theories, including the most general self-interacting scalar fields in four and three dimensions and fermions in two dimensions, have a simplified renormalization structure. For example, in…
We construct several charged regular black hole metrics employing mass distribution functions which are inspired by continuous probability distributions. Some of these metrics satisfy the weak energy condition and asymptotically behave as…
The objective is to investigate the global existence of solutions for a degenerate chemotaxis system with logistic sources in a two-dimensional domain. It is demonstrated that the inclusion of logistic sources can exclude the occurrence of…
A new three dimensional model of the FEL is presented. A system of scaled, coupled Maxwell Lorentz equations are derived in the paraxial limit. A minimal number of limiting assumptions are made and the equations are not averaged in the…