scholarly journals On weak (measure-valued)-strong uniqueness for compressible MHD system with non-monotone pressure law

2022 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Yu Liu ◽  
Ting Zhang
Keyword(s):  
Energy Inequality ◽  
Relative Energy ◽  
Mhd Equations ◽  
Strong Uniqueness ◽  
Uniqueness Property ◽  
Mhd System

<p style='text-indent:20px;'>In this paper, we define a renormalized dissipative measure-valued (rDMV) solution of the compressible magnetohydrodynamics (MHD) equations with non-monotone pressure law. We prove the existence of the rDMV solutions and establish a suitable relative energy inequality. And we obtain the weak (measure-valued)-strong uniqueness property of this rDMV solution with the help of the relative energy inequality.</p>

scholarly journals Global stability solution of the 2D MHD equations with mixed partial dissipation

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Yana Guo ◽  
Yan Jia ◽  
Bo-Qing Dong
Keyword(s):  
Magnetic Field ◽  
Global Stability ◽  
Mhd Equations ◽  
Bootstrap Argument ◽  
Partial Dissipation ◽  
Background Magnetic Field ◽  
Mhd System

<p style='text-indent:20px;'>This paper is devoted to understanding the global stability of perturbations near a background magnetic field of the 2D magnetohydrodynamic (MHD) equations with partial dissipation. We establish the global stability for the solutions of the nonlinear MHD system by the bootstrap argument.</p>

scholarly journals Weak–strong uniqueness property for models of compressible viscous fluids near vacuum*

Nonlinearity ◽  
2021 ◽  
Vol 34 (9) ◽  
pp. 6627-6650
Author(s):  
Eduard Feireisl ◽  
Antonín Novotný
Keyword(s):  
Viscous Fluids ◽  
Strong Uniqueness ◽  
Uniqueness Property

scholarly journals On vanishing limits of the shear viscosity and Hall coefficients for the planar compressible Hall-MHD system

2021 ◽  
Author(s):  
Xia Ye ◽  
Zejia Wang
Keyword(s):  
Boundary Layer ◽  
Shear Viscosity ◽  
Strong Solutions ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Mhd Equations ◽  
Layer Function ◽  
Mhd System ◽  
Initial Boundary Value ◽  
Hall Mhd

This paper deals with an initial-boundary value problem of the planar compressible Hall-magnetohydrodynamic (for short, Hall-MHD) equations. For the fixed shear viscosity and Hall coefficients, it is shown that the strong solutions of Hall-MHD equations and corresponding MHD equations are global. As both the shear viscosity and the Hall coefficients tend to zero, the convergence rate for the solutions from Hall-MHD equations to MHD equations is given. The thickness of boundary layer is discussed by spatially weighted estimation and the characteristic of boundary layer is described by constructing a boundary layer function.

scholarly journals Global well-posedness for the three-dimensional incompressible viscous non-resistive MHD equations in an infinite slab

2021 ◽  
Author(s):  
Youyi Zhao
Keyword(s):  
Initial Data ◽  
Three Dimensional ◽  
Mhd Equations ◽  
Well Posedness ◽  
Lagrangian Coordinates ◽  
Mathematical Approach ◽  
Compatibility Conditions ◽  
Finite Height ◽  
Infinite Slab ◽  
Mhd System

In this paper, we investigate the global well-posedness of the system of incompressible viscous non-resistive MHD fluids in a three-dimensional horizontally infinite slab with finite height. We reformulate our analysis to Lagrangian coordinates, and then develop a new mathematical approach to establish global well-posedness of the MHD system, which requires no nonlinear compatibility conditions on the initial data.

Long time behavior of solutions to 3D generalized MHD equations

2020 ◽  
Vol 32 (4) ◽  
pp. 977-993
Author(s):  
Xiaopeng Zhao
Keyword(s):  
Fractional Laplacian ◽  
Mhd Equations ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Algebraic Decay ◽  
Generalized Mhd Equations ◽  
Long Time ◽  
Whole Space ◽  
Mhd System ◽  
Incompressible Mhd

AbstractIn this paper, we consider the long time behavior of solutions for 3D incompressible MHD equations with fractional Laplacian. Firstly, in a periodic bounded domain, we prove the existence of a global attractor. The analysis reveals a relation between the Laplacian exponent and the regularity of the spaces of velocity and magnetic fields. Finally, in the whole space {\mathbb{R}^{3}}, we establish the sharp algebraic decay rate of solutions to the generalized MHD system provided that the parameters satisfy {\alpha,\beta\in(0,2]}.

scholarly journals THE ARTIFICIAL COMPRESSIBILITY APPROXIMATION FOR MHD EQUATIONS IN UNBOUNDED DOMAIN

2013 ◽  
Vol 10 (01) ◽  
pp. 181-198 ◽  
Author(s):  
DONATELLA DONATELLI
Keyword(s):  
Wave Equation ◽  
Weak Solution ◽  
Unbounded Domains ◽  
Mhd Equations ◽  
Magnetohydrodynamic Equations ◽  
Artificial Compressibility ◽  
Dispersive Estimate ◽  
Artificial Compressibility Method ◽  
Mhd System ◽  
Incompressible Magnetohydrodynamic Equations

We analyze a method of 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 compressibility method adapted to the MHD system. By exploiting the wave equation structure of the approximating system we achieve the convergence of the approximating sequences by means of dispersive estimate of Strichartz type. We prove that the soleinoidal component of the approximating velocity and magnetic fields is relatively compact and converges strongly to a weak solution of the MHD equation.

On the Uniqueness Property for Products of Symmetric Invariant Probability Measures

2002 ◽  
Vol 9 (1) ◽  
pp. 75-82
Author(s):  
A. Kharazishvili
Keyword(s):  
Probability Measure ◽  
Invariant Probability Measure ◽  
Probability Measures ◽  
Strong Uniqueness ◽  
Uniqueness Property

Abstract Two symmetric invariant probability measures μ 1 and μ 2 are constructed such that each of them possesses the strong uniqueness property but their product μ 1 × μ 2 turns out to be a symmetric invariant probability measure without the uniqueness property.

scholarly journals Weak-Strong Uniqueness for Compressible Magnetohydrodynamic Equations with Coulomb Force

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Lianhua He ◽  
Yonghui Zhou
Keyword(s):  
Relative Entropy ◽  
Coulomb Force ◽  
Two Dimensional ◽  
Strong Uniqueness ◽  
Magnetohydrodynamic Equations ◽  
Uniqueness Property ◽  
Magnetohydrodynamic System

In this paper, we consider the two-dimensional compressible magnetohydrodynamic system with Coulomb force. We apply the method of relative entropy to establish the weak-strong uniqueness property of this system.

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