Global well-posedness for the 3-D MHD equations with partial diffusion in the periodic domain

DOI10.1007/s11425-021-1861-yzbMath1489.35200OpenAlexW3197983764MaRDI QIDQ2078988

Wenji Chen, Jianfeng Zhou, Zhifei Zhang

Publication date: 4 March 2022

Published in: Science China. Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11425-021-1861-y

zbMATH Keywords

global well-posednessMHD equationsDiophantine condition

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Magnetohydrodynamics and electrohydrodynamics (76W05) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)

Related Items (12)

The MHD equations in the Lorentz space with time dependent external forces ⋮ Nonlinear stability for the 2D incompressible MHD system with fractional dissipation in the horizontal direction ⋮ Stability of 2D inviscid MHD equations with only vertical magnetic diffusion on T2 ⋮ Global small solutions to the 3D compressible viscous non-resistive MHD system ⋮ Global existence and decay estimate of solution to rate type viscoelastic fluids ⋮ Stability for the 2D incompressible MHD equations with only magnetic diffusion ⋮ Global smooth solutions to the 3D compressible viscous non-isentropic magnetohydrodynamic flows without magnetic diffusion ⋮ Stability and exponential decay for magnetohydrodynamic equations ⋮ Stability and optimal decay for the 3D magnetohydrodynamic equations with only horizontal dissipation ⋮ Optimal decay rates for \(n\)-dimensional generalized magnetohydrodynamic equations ⋮ Nonlinear stability of the inviscid magnetic Bénard problem ⋮ Stability and large time decay for the three-dimensional anisotropic magnetohydrodynamic equations

Cites Work

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• Longtime Dynamics of a Conductive Fluid in the Presence of a Strong Magnetic Field
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• Global Well-Posedness for the 2-D MHD Equations with Magnetic Diffusion
• On Current Developments in Partial Differential Equations
• Global Small Solutions to an MHD‐Type System: The Three‐Dimensional Case

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