Related papers: The three dimensional magneto-hydrostatic equation…
We present a method that gives highly accurate electrostatic potentials for systems where we have periodic boundary conditions in two spatial directions but free boundary conditions in the third direction. These boundary conditions are…
We consider the most general class of linear boundary-value problems for higher-order ordinary differential systems whose solutions and right-hand sides belong to the corresponding Sobolev spaces. For parameter-dependent problems from this…
This paper concerns the viscous and non-resistive MHD systems which govern the motion of electrically conducting fluids interacting with magnetic fields. We consider an initial-boundary value problem for both compressible and…
Based on the Newton's second law and the Maxwell equations for the electromagnetic fields, we establish a new 3D incompressible magneto-hydrodynamics(MHD) equations for the motion of plasma under the standard Coulomb gauge. By using the…
We study second-order hyperbolic equations with degenerate elliptic operators and non-homogeneous Dirichlet boundary inputs. We establish existence and regularity of weak solutions in weighted Sobolev spaces under mild assumptions on the…
This paper investigates the existence and uniqueness of local strong solutions to the three-dimensional compressible magnetohydrodynamic (MHD) equations with density-dependent viscosities in an exterior domain. The system models the…
We prove the well--posedness of a dynamical perfect plasticity model under general assumptions on the stress constraint set and on the reference configuration. The problem is studied by combining both calculus of variations and hyperbolic…
Numerical methods for solving the ideal magnetohydrodynamic (MHD) equations in more than one space dimension must confront the challenge of controlling errors in the discrete divergence of the magnetic field. One approach that has been…
We study the global stability of large solutions to the compressible isentropic magnetohydrodynamic equations in a three-dimensional (3D) bounded domain with Navier-slip boundary conditions. It is shown that the solutions converge to an…
A new conservative finite element solver for the three-dimensional steady magnetohydrodynamic (MHD) kinematics equations is presented.The solver utilizes magnetic vector potential and current density as solution variables, which are…
We consider the free boundary problem for relativistic plasma--vacuum interfaces in two and three spatial dimensions. The plasma flow is governed by the equations of ideal relativistic magnetohydrodynamics, while the vacuum magnetic and…
We study the global well-posedness of magnetohydrodynamic (MHD) equations. The hydrodynamic system consists of the Navier-Stokes equations for the fluid velocity coupled with a reduced from of the Maxwell equations for the magnetic field.…
We present three-dimensional simulations of Einstein equations implementing a symmetric hyperbolic system of equations with dynamical lapse. The numerical implementation makes use of techniques that guarantee linear numerical stability for…
A parabolic free boundary problem modeling a three-dimensional electrostatic MEMS device is investigated. The device is made of a rigid ground plate and an elastic top plate which is hinged at its boundary, the plates being held at…
This paper introduces and analyses the new grid-based tensor approach to approximate solution of the elliptic eigenvalue problem for the 3D lattice-structured systems. We consider the linearized Hartree-Fock equation over a spatial…
In the present work we investigate the Tricomi problem with integral gluing condition for parabolic-hyperbolic equation with the Caputo fractional order derivative. Using the method of energy integrals we prove the uniqueness of the…
This paper is concerned with the incompressible limit of the compressible magnetohydrodynamic equations with periodic boundary conditions. It is rigorously shown that the weak solutions of the compressible magnetohydrodynamic equations…
A first-order elliptic-hyperbolic system in extended projective space is shown to possess strong solutions to a natural class of Guderley-Morawetz-Keldysh problems on a typical domain.
We study the solvability of boundary-value problems for differential-operator equations of the second order in L p (0, 1; X), with 1 < p < +$\infty$, X being a UMD complex Banach space. The originality of this work lies in the fact that we…
In this work we study linear Maxwell equations with time- and space-dependent matrix-valued permittivity and permeability on domains with a perfectly conducting boundary. This leads to an initial boundary value problem for a first order…