Related papers: On convergence of numerical solutions for the comp…
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…
Numerical methods for solving the ideal magnetohydrodynamic (MHD) equations in more than one space dimension must either confront the challenge of controlling errors in the discrete divergence of the magnetic field, or else be faced with…
We study the initial-boundary value problem for 1D compressible MHD equations of viscous non-resistive fluids in the Lagrangian mass coordinates. Based on the estimates of upper and lower bounds of the density, weak solutions are…
This paper addresses the three concepts of \textit{ consistency, stability and convergence } in the context of compact finite volume schemes for systems of nonlinear hyperbolic conservation laws. The treatment utilizes the framework of…
We propose a new concept of weak solution to the equations of compressible magnetohydrodynamics driven by large boundary data. The system of the underlying field equations is solvable globally in time in the out of equilibrium regime…
This paper examines the uniqueness of weak solutions to the d-dimensional magnetohydrodynamic (MHD) equations with the fractional dissipation $(-\Delta)^\alpha u$ and without the magnetic diffusion. Important progress has been made on the…
We propose several continuous data assimilation (downscaling) algorithms based on feedback control for the 2D magnetohydrodynamic (MHD) equations. We show that for sufficiently large choices of the control parameter and resolution and…
In this paper we prove the existence of global weak dissipative martingale solutions for a one-dimensional compressible fluid model with capillarity and density dependent viscosity, driven by random initial data and a stochastic forcing…
A new fully discrete linearized $H^1$-conforming Lagrange finite element method is proposed for solving the two-dimensional magneto-hydrodynamics equations based on a magnetic potential formulation. The proposed method yields numerical…
In this paper, we are concerned with the compressible viscous magnetohydrodynamic (MHD) system and investigate the large time behavior of strong solutions near constant equilibrium. In the eighties, Umeda, Kawashima and Shizuta initiated…
We consider the motion of an inviscid compressible fluid under the mutual interactions with magnetic field. We show that the initial value problem is ill--posed in the class of weak solutions for a large class of physically admissible data.…
In this paper we analyze a method of to approximation for the weak solutions of the incompressible magnetohydrodynamic equations (MHD) in unbounded domains. In particular we describe an hyperbolic version of the so called artificial…
We are concerned with the study of the Cauchy problem to the 3D compressible Hall-magnetohydrodynamic system. We first establish the unique global solvability of strong solutions to the system when the initial data are close to a stable…
We propose a concept of dissipative weak (DW) solutions for the Navier-Stokes-Korteweg (NSK) system and prove conditional convergence of a structure-preserving finite volume scheme towards such a solution. DW solutions provide a generalized…
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…
The full compressible magnetohydrodynamic equations can be derived formally from the complete electromagnetic fluid system in some sense as the dielectric constant tends to zero. This process is usually referred as magnetohydrodynamic…
This paper is concerned with the incompressible limit of the compressible magnetohydrodynamic equations with vanishing viscosity coefficients and general initial data in the whole space $\mathbb{R}^d$ $ (d=2$ or 3). It is rigorously showed…
A numerical method based on the hybridizable discontinuous Galerkin method in space and backward Euler in time is formulated and analyzed for solving the miscible displacement problem. Under low regularity assumptions, convergence is…
We construct weak solutions to the ideal magneto-hydrodynamic (MHD) equations which have finite total energy, and whose magnetic helicity is not a constant function of time. In view of Taylor's conjecture, this proves that there exist…
In this paper, we consider the full compressible, viscous, non-resistive MHD system under the assumption that the fluids move on a plane while the magnetic field is oriented vertically. Within the framework of Besov spaces, by introducing…