Global regularity for the 3D MHD system with damping

Zhang, Zujin; Yang, Xian

doi:10.4064/cm6654-9-2015

Cited by 3 publications

(4 citation statements)

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“…He considered the system with nonlinear damping in the equations for both the velocity field (with nonlinear damping parameter α) and the magnetic field (with parameter β), and he proved existence and uniqueness of global strong solutions in the full space case for several ranges of parameters, most interestingly for our purposes for α, β ≥ 4. Zhang and Yang [54] tried to improve this to α, β > 3, but apparently made a mistake in their proof [52, Remark after Equation (9), p. 2]. Zhang et al [52] then improved the range to α ∈ [3, 27 8 ], β ≥ 4.…”

Section: Damped Navier-stokes Equations (Or Bfed Models)mentioning

confidence: 99%

“…Moreover, we describe the magnetic pressure problem in regularised MHD equations. Furthermore, our work basically provides the critical case α = β = 3 of the model considered in [48,52,54].…”

Section: Theorem 4 (Convergence To the Untamed Equations)mentioning

confidence: 99%

“…The first term of the last line here cancels with the second term of (54). Thus, we only have to deal with the first term of (54):…”

Section: Convergence To the Untamed Mhd Equationsmentioning

confidence: 99%

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The tamed MHD equations

Schenke

2020

J. Evol. Equ.

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We study a regularised version of the magnetohydrodynamics (MHD) equations, the tamed MHD (TMHD) equations. They are a model for the flow of electrically conducting fluids through porous media. We prove existence and uniqueness of TMHD on the whole space $${\mathbb {R}}^{3}$$ R 3 , that smooth data give rise to smooth solutions and show that solutions to TMHD converge to a suitable weak solution of the MHD equations as the taming parameter N tends to infinity. Furthermore, we adapt a regularity result for the Navier–Stokes equations to the MHD case.

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Section: Damped Navier-stokes Equations (Or Bfed Models)mentioning

confidence: 99%

Section: Theorem 4 (Convergence To the Untamed Equations)mentioning

confidence: 99%

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The tamed MHD equations

Schenke

2020

J. Evol. Equ.

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“…Z.J. Zhang and X. Yang [54] tried to improve this to α, β > 3, but apparently made a mistake in their proof ( [52, Remark after Equation (9), p. 2]). Z.J.…”

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confidence: 99%

The Tamed MHD Equations

Schenke

2020

Preprint

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We study a regularised version of the magnetohydrodynamics (MHD) equations, the tamed MHD (TMHD) equations. They are a model for the flow of electrically conducting fluids through porous media. We prove existence and uniqueness of TMHD on the whole space R 3 , that smooth data give rise to smooth solutions, and show that solutions to TMHD converge to a suitable weak solution of the MHD equations as the taming parameter N tends to infinity. Furthermore, we adapt a regularity result for the Navier-Stokes equations to the MHD case.

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Long-time behavior for 3D MHD equations with nonlinear damping

Song

Xiong

2022

Journal of Mathematical Analysis and Applications

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Global regularity for the 3D MHD system with damping

Cited by 3 publications

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The tamed MHD equations

The tamed MHD equations

The Tamed MHD Equations

Long-time behavior for 3D MHD equations with nonlinear damping

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