Stability of stationary solution for the compressible viscous magnetohydrodynamic equations with large potential force in bounded domain

Li, Yeping; Yang, Xiongfeng

doi:10.1016/j.jde.2016.11.021

Cited by 8 publications

(2 citation statements)

References 33 publications

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“…In this paper, we consider the following compressible magnetohydrodynamic equations in

R^{3}

(see other studies() for instance):

ρ_{t} + div false(ρ u false) = 0,

ρ u_{t} + div false(ρ u \otimes u false) + \nabla P false(ρ false) = false(\nabla \times H false) \times H + μ normalΔ u + false(μ + λ false) \nabla div u + ρ f,

H_{t} - \nabla \times false(u \times H false) = - \nabla \times false(ν \nabla \times H false),

div H = 0,

with

x = false(x_{1}, x_{2}, x_{3} false) \in R^{3}

, t ≥ 0. The unknown functions ρ , u = ( u 1 , u 2 , u 3 ), P , H = ( H 1 , H 2 , H 3 ), and f = ( f 1 , f 2 , f 3 ) represent the density, the velocity, the pressure, the magnetic field, and the (assigned) external force field, respectively.…”

Section: Introductionmentioning

confidence: 99%

“…Assume that the large potential force satisfy f = ( f 1 ( x ), f 2 ( x ), f 3 ( x )), Li and Yang studied the well‐posedness of the initial boundary value problem for the compressible viscous MHD equations provided that the initial data are close to the stationary solution. However, the condition that the initial density ρ 0 in Li and Yang has positive lower bound is quite essential, ie, no vacuum at any point.…”

Section: Introductionmentioning

confidence: 99%

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Global well‐posedness of classical solutions to 3D compressible magnetohydrodynamic equations with large potential force

Lin

Huang

2018

Math Methods in App Sciences

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We consider the Cauchy problem of isentropic compressible magnetohydrodynamic equations with large potential force in R 3 . When the initial data ( 0 , u 0 , H 0 ) is of small energy, we investigate the global well-posedness of classical solutions where the flow density is allowed to contain vacuum states. KEYWORDSCauchy problem, compressible magnetohydrodynamic equations, global classical solution, vacuum divH = 0, (1.4) with x = (x 1 , x 2 , x 3 ) ∈ R 3 , t ≥ 0. The unknown functions , u = (u 1 , u 2 , u 3 ), P, H = ( H 1 , H 2 , H 3 ), and f = (f 1 , f 2 , f 3 ) represent the density, the velocity, the pressure, the magnetic field, and the (assigned) external force field, respectively. In addition, the pressure is given by P( ) = a with a > 0, > 1, the viscosity coefficients and satisfy > 0, 3 + 2 ≥ 0, (1.5)Math Meth Appl Sci. 2019;42:747-766. wileyonlinelibrary.com/journal/mma

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“…In this paper, we consider the following compressible magnetohydrodynamic equations in

R^{3}

(see other studies() for instance):

ρ_{t} + div false(ρ u false) = 0,

ρ u_{t} + div false(ρ u \otimes u false) + \nabla P false(ρ false) = false(\nabla \times H false) \times H + μ normalΔ u + false(μ + λ false) \nabla div u + ρ f,

H_{t} - \nabla \times false(u \times H false) = - \nabla \times false(ν \nabla \times H false),

div H = 0,

with

x = false(x_{1}, x_{2}, x_{3} false) \in R^{3}

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Global well‐posedness of classical solutions to 3D compressible magnetohydrodynamic equations with large potential force

Lin

Huang

2018

Math Methods in App Sciences

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On a Non-conservative Compressible Two-Fluid Model in a Bounded Domain: Global Existence and Uniqueness

Wang

Wen

Yao

2020

J. Math. Fluid Mech.

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On the Steady Flows of Viscous Compressible Magnetohydrodynamic Equations in an Infinite Horizontal Layer

Benabidallah,

Ebobisse

2024

J. Math. Fluid Mech.

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We consider in an infinite horizontal layer the stationary motion of a viscous compressible fluid in a magnetic field subject to the gravitational force, where the Dirichlet boundary condition for the velocity and similar but non-homogeneous and large enough conditions for the magnetic field are assumed. Existence of a stationary solution in a neighborhood close to the equilibrium state is obtained in Sobolev spaces as limit of a sequence of fixed points of some suitable operators.

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Stability of stationary solution for the compressible viscous magnetohydrodynamic equations with large potential force in bounded domain

Cited by 8 publications

References 33 publications

Global well‐posedness of classical solutions to 3D compressible magnetohydrodynamic equations with large potential force

Global well‐posedness of classical solutions to 3D compressible magnetohydrodynamic equations with large potential force

On a Non-conservative Compressible Two-Fluid Model in a Bounded Domain: Global Existence and Uniqueness

On the Steady Flows of Viscous Compressible Magnetohydrodynamic Equations in an Infinite Horizontal Layer

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