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The issue of a self-consistent solution of Maxwell-Einstein equations achieves a very simple form when all quantum effects are neglected but a weak vacuum polarization due to an external magnetic field is taken into account. From a…
This paper focuses on the 2D compressible magnetohydrodynamic (MHD) equations without magnetic diffusion in a periodic domain. We present a systematic approach to establishing the global existence of smooth solutions when the initial data…
This paper is devoted to the study of the weak-strong uniqueness property for the full compressible magnetohydrodynamics flows. The governing equations for magnetohydrodynamic flows are expressed by the full Navier-Stokes system for…
In this article we prove the global existence of weak solutions for a diffuse interface model in a bounded domain (both in 2D and 3D) involving incompressible magnetic fluids with unmatched densities. The model couples the incompressible…
We analyze the anisotropy of turbulence in an electrically conducting fluid in the presence of a uniform magnetic field, for low magnetic Reynolds number, using the quasi-static approximation. In the linear limit, the kinetic energy of…
In one-dimensional unbounded domains, we consider the equations of a planar compressible magnetohydrodynamic (MHD) flow with constant viscosity and heat conductivity. More precisely, we prove the global existence of strong solutions to the…
The aim of this article is to investigate the well-posedness, stability and convergence of solutions to the time-dependent Maxwell's equations for electric field in conductive media in continuous and discrete settings. The situation we…
This article is devoted to the derivation and analysis of a system of partial differential equations modeling a diffuse interface flow of two Newtonian incompressible magnetic fluids. The system consists of the incompressible Navier-Stokes…
We present an abstract framework for parabolic type equations which possibly degenerate on certain spatial regions. The degeneracies are such that the equations under investigation may admit a type change ranging from parabolic to elliptic…
In this paper, we investigate the solvability, regularity and the vanishing dissipation limit of solutions to the three-dimensional viscous magneto-hydrodynamic (MHD) equations in bounded domains. On the boundary, the velocity field…
The linear marginal instability of an MHD Taylor-Couette flow of infinite vertical extension is considered. For hydrodynamically unstable flows the minimum Reynolds number exists even without a magnetic field, but there are also solutions…
Extensive research papers of three-dimensional computational techniques are widely used for the investigation of human brain pathophysiology. Eddy current analyzing could provide an indication of conductivity change within a biological…
We present a hydrodynamic theory for electron-hole magnetotransport in graphene incorporating carrier-population imbalance, energy, and momentum relaxation processes. We focus on the electric response and find that the carrier and energy…
We investigate the large-scale transport properties of quasi-neutrally-buoyant inertial particles carried by incompressible zero-mean periodic or steady ergodic flows. We show how to compute large-scale indicators such as the…
We consider the electron magnetohydrodynamics (MHD) with static background ion flow. A special situation of $B(x,y,t)=\nabla\times (a\vec e_z)+b \vec e_z$ with scalar-valued functions $a(x,y,t)$ and $b(x,y,t)$ was studied numerically in the…
We study the equations of a two dimensional incompressible Newtonian fluid coupled with a dispersive parabolic-elliptic system on bounded domains. Global in time weak solutions are shown to exist and converge with a rate to the stationary…
The possibility of the existence of quasi-stationary electromagnetic fields in plasma supported by their own self-consistent current follows from Maxwell's equations with field sources. These equations also give rise to a wave equation for…
We consider the stochastic electrokinetic flow in a smooth bounded domain $\mathcal{D}$, modelled by a Nernst-Planck-Navier-Stokes system with a blocking boundary conditions for ionic species concentrations, perturbed by multiplicative…
The purpose of this work is to prove existence of a weak solution of the two dimensional incompressible Euler equations on a noncylindrical domain consisting of a smooth, bounded, connected and simply connected domain undergoing a…
Axial flux permanent magnet designs are compact and becoming an attractive design for electric vehicles as an auxiliary braking system. This work develops the design of an Axial Flux Permanent Magnet Eddy current brake for application on…