Related papers: Existence and regularity for eddy currents system …
We study the electron magnetohydrodynamics (MHD) in two dimensional geometry, which has a rich family of steady states. In an anisotropic resistivity context, we show global in time existence of small smooth solution near a shear type…
Eddy current shielding by a Faraday cage is an effective way to shield alternating-current (AC) magnetic fields in scientific instrumentation. In a strong static magnetic field, however, the eddy current in the conductive shield is subject…
Motivated by some models arising in quantum plasma dynamics, in this paper we study the Maxwell-Schr\"odinger system with a power-type nonlinearity. We show the local well-posedness in $H^2(\mathbb{R}^3)\times H^{3/2}(\mathbb{R}^3)$ and the…
We are concerned with a model of ideal compressible isentropic two-fluid magnetohydrodynamics (MHD). Introducing an entropy-like function, we reduce the equations of two-fluid MHD to a symmetric form which looks like the classical MHD…
We consider the time-harmonic Maxwell equations set on a domain made up of two subdomains that represent a magnetic conductor and a non-magnetic material, and we assume that the relative magnetic permeability $\mu_{r}$ between the two…
Eddy current separation (ECS) is a process used throughout the scrap recycling industry for separating nonferrous metals from nonmetallic fluff. To date, however, the physical theory of ECS has generally been limited to empirical…
In our previous work (arXiv:2510.00812), we have shown the global existence and incompressible limit of weak solutions to the isentropic compressible magnetohydrodynamic equations involving ripped density and large initial energy in the…
We investigate the compressible magnetohydrodynamic equations subject to large external potential forces with discontinuous initial data in a three-dimensional bounded domain under Navier-slip boundary conditions. We show the global…
For a reduced Ginzburg-Landau model in which the magnetic field is neglected, we prove, for weak electric currents, the existence of a steady-state solution in a vicinity of the purely superconducting state. We further show that this…
Magnetic induction in magnetohydrodynamic fluids at magnetic Reynolds number (Rm) less than~1 has long been known to cause magnetic drag. Here, we show that when $\mathrm{Rm} \gg 1$ and the fluid is in a hydrodynamic-dominated regime in…
In this paper we initiate the mathematical analysis of a system of nonlinear Stochastic Partial Differential equations describing the motion of turbulent Non-Newtonian media in the presence of fluctuating magnetic field. The system is…
The eddy current problem has many relevant practical applications in science, ranging from non-destructive testing to magnetic confinement of plasma in fusion reactors. It arises when electrical conductors are immersed in an external…
This paper investigates the non-resistive compressible magnetohydrodynamic (MHD) equations in $\mathbb{R}^2$. We establish the global existence and stability of classical solutions for initial data sufficiently close to a constant…
The existence of global-in-time classical solutions to the Cauchy problem of compressible magnetohydrodynamic flows with zero magnetic diffusivity is considered in two dimensions. The linear structure is a degenerated hyperbolic-parabolic…
We address a threshold problem of the Couette flow $(y,0)$ in a uniform magnetic field $(\beta,0)$ for the 2D MHD equation on $\mathbb{T}\times\mathbb{R}$ with fluid viscosity $\nu$ and magnetic resistivity $\mu$. The nonlinear enhanced…
We present two models for turbulent flows with periodic boundary conditions and with either rotation, or a magnetic field in the magnetohydrodynamics (MHD) limit. One model, based on Lagrangian averaging, can be viewed as an…
Many earlier works were devoted to the study of the breakdown of superconductivity in type-II superconducting bounded planar domains, submitted to smooth magnetic fields. In the present contribution, we consider a new situation where the…
Consider the time-periodic viscous incompressible fluid flow past a body with non-zero velocity at infinity. This article gives sufficient conditions such that weak solutions to this problem are smooth. Since time-periodic solutions do not…
In this paper, we prove the existence of two-dimensional solutions to the steady Euler-Poisson system with continuous transonic transitions across sonic interfaces of codimension 1. First, we establish the well-posedness of a boundary value…
This work presents a high-order isogeometric formulation for magnetoquasistatic eddy-current problems based on a decomposition into Biot-Savart-driven source fields and finite-element reaction fields. Building upon a recently proposed…