Global Existence and Large-Time Behavior of Solutions to the Three-Dimensional Equations of Compressible Magnetohydrodynamic Flows

Hu, Xianpeng; Wang, Dehua

doi:10.1007/s00205-010-0295-9

Cited by 319 publications

(225 citation statements)

References 22 publications

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“…The higher order energies are defined as: For r ≥ 1 13) where I(r) = 0 if r = 1 and I(r) = 1 for r > 1, so we do not need the boundary integral for r = 1,…”

Section: B|mentioning

confidence: 99%

A Priori Estimates for Free Boundary Problem of Incompressible Inviscid Magnetohydrodynamic Flows

Hao

Luo

2014

Arch Rational Mech Anal

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Abstract. In the present paper, we prove the a priori estimates of Sobolev norms for a free boundary problem of the incompressible inviscid MHD equations in all physical spatial dimensions n = 2 and 3 by adopting a geometrical point of view used in [4], and estimating quantities such as the second fundamental form and the velocity of the free surface. We identify the well-posedness condition that the outer normal derivative of the total pressure including the fluid and magnetic pressures is negative on the free boundary, which is similar to the physical condition (Taylor sign condition) for the incompressible Euler equations of fluids.

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“…The higher order energies are defined as: For r ≥ 1 13) where I(r) = 0 if r = 1 and I(r) = 1 for r > 1, so we do not need the boundary integral for r = 1,…”

Section: B|mentioning

confidence: 99%

A Priori Estimates for Free Boundary Problem of Incompressible Inviscid Magnetohydrodynamic Flows

Hao

Luo

2014

Arch Rational Mech Anal

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“…For the existence of solutions to MHD, Chen and Wang [7] showed the existence of global solutions to the piston problem. Hu and Wang [8] obtained the existence of global weak solutions in three dimensions for MHD equations, by using the Faedo-Galerkin method. Many authors have investigated the existence of global solutions to viscous systems.…”

Section: Introductionmentioning

confidence: 99%

Existence of Global Solutions for Nonlinear Magnetohydrodynamics with Finite Larmor Radius Corrections

Elsrrawi

Hattori

2018

International Journal of Differential Equations

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We discuss the existence of global solutions to the magnetohydrodynamics (MHD) equations, where the effects of finite Larmor radius corrections are taken into account. Unlike the usual MHD, the pressure is a tensor and it depends on not only the density but also the magnetic field. We show the existence of global solutions by the energy methods. Our techniques of proof are based on the existence of local solution by semigroups theory and a priori estimate.

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“…We first notice that the global-in-time existence solutions for systems ( (1)- (3)), supplemented with physically relevant constitutive relations, has been studied by Hu and Wang [1].…”

Section: Introductionmentioning

confidence: 99%

Singular Limit of the Rotational Compressible Magnetohydrodynamic Flows

Kwon¹

2017

Advances in Mathematical Physics

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We consider the compressible models of magnetohydrodynamic flows giving rise to a variety of mathematical problems in many areas. We derive a rigorous quasi-geostrophic equation governed by magnetic field from the stratified flows of the rotational compressible magnetohydrodynamic flows with the well-prepared initial data and the tool of proof is based on the relative entropy. Furthermore, the convergence rates are obtained.

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Global Existence and Large-Time Behavior of Solutions to the Three-Dimensional Equations of Compressible Magnetohydrodynamic Flows

Cited by 319 publications

References 22 publications

A Priori Estimates for Free Boundary Problem of Incompressible Inviscid Magnetohydrodynamic Flows

A Priori Estimates for Free Boundary Problem of Incompressible Inviscid Magnetohydrodynamic Flows

Existence of Global Solutions for Nonlinear Magnetohydrodynamics with Finite Larmor Radius Corrections

Singular Limit of the Rotational Compressible Magnetohydrodynamic Flows

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